# Hisham SatiNew York University Abu Dhabi · Mathematics

Hisham Sati

PhD

## About

126

Publications

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Citations since 2016

## Publications

Publications (126)

While the realization of scalable quantum computation will arguably require topological stabilization and, with it, topological-hardware-aware quantum programming and topological-quantum circuit verification, the proper combination of these strategies into dedicated topological quantum programming languages has not yet received attention. Here we d...

While the classification of non-interacting crystalline topological insulator phases by equivariant K-theory has become widely accepted, its generalization to anyonic interacting phases -- hence to phases with topologically ordered ground states supporting topological braid quantum gates -- has remained wide open. On the contrary, the success of K-...

We characterize the integral cohomology and the rational homotopy type of the maximal Borel-equivariantization of the combined Hopf/twistor fibration, and find that subtle relations satisfied by the cohomology generators are just those that govern Hořava–Witten’s proposal for the extension of the Green–Schwarz mechanism from heterotic string theory...

We demonstrate that twisted equivariant differential K-theory of transverse complex curves accommodates exotic charges of the form expected of codimension=2 defect branes, such as of D7-branes in IIB/F-theory on A-type orbifold singularities, but also of their dual 3-brane defects of class-S theories on M5-branes. These branes have been argued, wit...

In this book we prove the classification theorem for equivariant principal bundles in the case that the topological structure group is truncated. The result is proven in a conceptually transparent manner as a consequence of a smooth Oka principle, which becomes available after faithfully embedding traditional equivariant topology into the singular-...

Mysterious duality has been discovered by Iqbal, Neitzke, and Vafa in 2001 as a convincing, yet mysterious correspondence between certain symmetry patterns in toroidal compactifications of M-theory and del Pezzo surfaces, both governed by the root system series $E_k$. It turns out that the sequence of del Pezzo surfaces is not the only sequence of...

We highlight what seems to be a remaining subtlety in the argument for the cancellation of the total anomaly associated with the M5-brane in M-theory. Then, we prove that this subtlety is resolved under the hypothesis that the C-field flux is charge-quantized in the generalized cohomology theory called J-twisted cohomotopy.

A new super-exceptional embedding construction of the heterotic M5-brane's sigma-model was recently shown to produce, at leading order in the super-exceptional vielbein components, the super-Nambu-Goto (Green-Schwarz-type) Lagrangian for the embedding fields plus the Perry-Schwarz Lagrangian for the free abelian self-dual higher gauge field. Beyond...

We provide several constructions in differential KO-theory. First, we construct a differential refinement of the Aˆ-genus and a pushforward leading to a Riemann-Roch theorem. We set up a differential refinement of the Atiyah-Hirzebruch spectral sequence (AHSS) for differential KO-theory and explicitly identify the differentials, including ones whic...

Weight systems on chord diagrams play a central role in knot theory and Chern-Simons theory; and more recently in stringy quantum gravity. We highlight that the noncommutative algebra of horizontal chord diagrams is canonically a star-algebra, and ask which weight systems are positive with respect to this structure; hence we ask: Which weight syste...

The full 6d Hopf–Wess–Zumino term in the action functional for the M5-brane is anomalous as traditionally defined. What has been missing is a condition implying the higher analogue of level quantization familiar from the 2d Wess–Zumino term. We prove that the anomaly cancellation condition is implied by the hypothesis that the C-field is charge-qua...

We show that charge-quantization of the M-theory C-field in J-twisted Cohomotopy implies the emergence of a higher Sp(1)-gauge field on single heterotic M5-branes, which exhibits a worldvolume Stringc2-structure.

In the quest for mathematical foundations of M-theory, the "Hypothesis H" that fluxes are quantized in Cohomotopy theory, implies, on flat but possibly singular spacetimes, that M-brane charges locally organize into equivariant homotopy groups of spheres. Here we show how this leads to a correspondence between phenomena conjectured in M-theory and...

We compare the description of the M-theory form fields via cohomotopy versus that via integral cohomology. The conditions for lifting the latter to the former are identified using obstruction theory in the form of Postnikov towers, where torsion plays a central role. A subset of these conditions are shown to correspond compatibly to existing consis...

The lift of K-theoretic D-brane charge to M-theory was recently hypothesized to land in Cohomotopy cohomology theory. To further check this Hypothesis H, here we explicitly compute the constraints on fractional D-brane charges at ADE-orientifold singularities imposed by the existence of lifts from equivariant K-theory to equivariant Cohomotopy theo...

The celebrated Green-Schwarz mechanism in heterotic string theory has been suggested to secretly underly a higher gauge theoretic phenomenon, embodying a higher Bianchi identity for a higher-degree analog of a curvature form of a higher gauge field. Here we prove that the non-perturbative Horava-Witten Green-Schwarz mechanism for heterotic line bun...

We extend the Chern character on K-theory, in its generalization to the Chern-Dold character on generalized cohomology theories, further to (twisted, differential) non-abelian cohomology theories, where its target is a non-abelian de Rham cohomology of twisted L-infinity algebra valued differential forms. The construction amounts to leveraging the...

We characterize the integral cohomology and the rational homotopy type of the maximal Borel-equivariantization of the combined Hopf/twistor fibration, and find that subtle relations satisfied by the cohomology generators are just those that govern Horava-Witten's proposal for the extension of the Green-Schwarz mechanism from heterotic string theory...

The concept of orbifolds should unify differential geometry with equivariant homotopy theory, so that orbifold cohomology should unify differential cohomology with proper equivariant cohomology theory. Despite the prominent role that orbifolds have come to play in mathematics and mathematical physics, especially in string theory, the formulation of...

We consider the hypothesis that the C-field 4-flux and 7-flux forms in M-theory are in the image of the non-abelian Chern character map from the non-abelian generalized cohomology theory called J-twisted Cohomotopy theory. We prove for M2-brane backgrounds in M-theory on 8-manifolds that such charge quantization of the C-field in Cohomotopy theory...

There are fundamental open problems in the precise global nature of RR-field tadpole cancellation conditions in string theory. Moreover, the non-perturbative lift as M5/MO5-anomaly cancellation in M-theory had been based on indirect plausibility arguments, lacking a microscopic underpinning in M-brane charge quantization. We provide a framework for...

A new super-exceptional embedding construction of the heterotic M5-brane's sigma-model was recently shown to produce, at leading order in the super-exceptional vielbein components, the super-Nambu-Goto (Green-Schwarz-type) Lagrangian for the embedding fields plus the Perry-Schwarz Lagrangian for the free abelian self-dual higher gauge field. Beyond...

We show that charge-quantization of the M-theory C-field in J-twisted Cohomotopy implies emergence of a higher Sp(1)-gauge field on single heterotic M5-branes, which exhibits worldvolume twisted String structure.

We highlight what seems to be a remaining subtlety in the argument for the cancellation of the total anomaly associated with the M5-brane in M-theory. Then we prove that this subtlety is resolved under the hypothesis that the C-field flux is charge-quantized in the generalized cohomology theory called J-twisted Cohomotopy.

A bstract
In the quest for the mathematical formulation of M-theory, we consider three major open problems: a first-principles construction of the single (abelian) M5-brane Lagrangian density, the origin of the gauge field in heterotic M-theory, and the supersymmetric enhancement of exceptional M-geometry. By combining techniques from homotopy theo...

We compare the description of the M-theory form fields via cohomotopy versus that via integral cohomology. The conditions for lifting the former to the latter are identified using obstruction theory in the form of Postnikov towers, where torsion plays a central role. A subset of these conditions are shown to correspond compatibly to existing consis...

We introduce a differential refinement of Cohomotopy cohomology theory, defined on Penrose diagram spacetimes, whose cocycle spaces are unordered configuration spaces of points. First we prove that charge quantization in this differential 4-Cohomotopy theory implies intersecting p/(p+2)-brane moduli given by ordered configurations of points in the...

A key open problem in M-theory is the identification of the degrees of freedom that are expected to be hidden at ADE-singularities in spacetime. Comparison with the classification of D-branes by K-theory suggests that the answer must come from the right choice of generalized cohomology theory for M-branes. Here we show that real equivariant Cohomot...

A key open problem in M-theory is to explain the mechanism of “gauge enhancement” through which M-branes exhibit the nonabelian gauge degrees of freedom seen perturbatively in the limit of 10d string theory. In fact, since only the twisted K-theory classes represented by nonabelian Chan–Paton gauge fields on D-branes have an invariant meaning, the...

There are fundamental open problems in the precise global nature of RR-field tadpole cancellation conditions in string theory. Moreover, the non-perturbative lift as M5/MO5-anomaly cancellation in M-theory had been based on indirect plausibility arguments,lacking a microscopic underpinning in M-brane charge quantization. We provide a framework for...

We consider the global aspects of the 6-dimensional $\mathcal{N}=(1, 0)$ theory arising from the coupling of the vector multiplet to the tensor multiplet. We show that the Yang-Mills field and its dual, when both are abelianized, combine to define a class in twisted cohomology with the twist arising from the class of the $B$-field, in a duality-sym...

In the quest for the mathematical formulation of M-theory, we consider three major open problems: a first-principles construction of the single (abelian) M5-brane Lagrangian density, the origin of the gauge field in heterotic M-theory, and the supersymmetric enhancement of exceptional M-geometry. By combining techniques from homotopy theory and fro...

The full 6d Wess-Zumino term in the action functional for the M5-brane is anomalous as traditionally defined. What has been missing is a condition implying the higher analogue of level quantization familiar from the 2d Wess-Zumino term. We prove that the anomaly cancellation condition is implied by the hypothesis that the C-field is charge-quantize...

We provide a systematic approach to twisting differential KO-theory leading to a construction of the corresponding twisted differential Atiyah-Hirzebruch spectral sequence (AHSS). We relate and contrast the degree two and the degree one twists, whose description involves appropriate local systems. Along the way, we provide a complete and explicit i...

We review how core structures of string/M‐theory emerge as higher structures in super homotopy theory; namely from systematic analysis of the brane bouquet of universal invariant higher central extensions growing out of the superpoint. Since super homotopy theory is immensely rich, to start with we consider this in the rational/infinitesimal approx...

We show that all the expected anomaly cancellations in M-theory follow from charge-quantizing the C-field in the non-abelian cohomology theory twisted Cohomotopy. Specifically, we show that such cocycles exhibit all of the following: (1) the half-integral shifted flux quantization condition, (2) the cancellation of the total M5-brane anomaly, (3) t...

We provide a systematic approach to describing the Ramond-Ramond (RR) fields as elements in twisted differential K-theory. This builds on a series of constructions by the authors on geometric and computational aspects of twisted differential K-theory, which to a large extent were originally motivated by this problem. In addition to providing a new...

We review how core structures of string/M-theory emerge as higher structures in super homotopy theory; namely from systematic analysis of the brane bouquet of universal invariant higher central extensions growing out of the superpoint. Since super homotopy theory is immensely rich, to start with we consider this in the rational/infinitesimal approx...

We describe an efficient algorithm that computes, for any finite group G, the linear span of its virtual permutation representations inside all its linear representations, hence the image of the canonical morphism $\beta$ from the Burnside ring to the representation ring. We use this to determine the image and cokernel of $\beta$ for binary Platoni...

In this note we provide a new perspective on the topological parts of several action functionals in string and M-theory. We show that rationally these can be viewed as large gauge transformations corresponding to variations of higher structures, such as String, Fivebrane, and Ninebrane structures.

In this note we provide a new perspective on the topological parts of several action functionals in string and M-theory. We show that rationally these can be viewed as large gauge transformations corresponding to variations of higher structures, such as String, Fivebrane, and Ninebrane structures.

We provide a systematic and detailed treatment of differential refinements of KO-theory. We explain how various flavors capture geometric aspects in different but related ways, highlighting the utility of each. While general axiomatics exist, no explicit constructions seem to have appeared before. This fills a gap in the literature in which K-theor...

A key open problem in M-theory is the mechanism of "gauge enhancement", which supposedly makes M-branes exhibit the nonabelian gauge degrees of freedom that are seen perturbatively in the limit of 10d string theory. In fact, since only the twisted K-theory classes represented by nonabelian Chan-Paton gauge fields on D-branes have invariant meaning,...

A key open problem in M-theory is the mechanism of "gauge enhancement", which supposedly makes M-branes exhibit the nonabelian gauge degrees of freedom that are seen perturbatively in the limit of 10d string theory. In fact, since only the twisted K-theory classes represented by nonabelian Chan-Paton gauge fields on D-branes have invariant meaning,...

A key open problem in M-theory is the identification of the degrees of freedom that are expected to be hidden at ADE-singularities in spacetime. Comparison with the classification of D-branes by K-theory suggests that the answer must come from the right choice of generalized cohomology theory for M-branes. Here we show that real equivariant cohomot...

By analyzing super-torsion and brane super-cocycles, we derive a new duality in M-theory, which takes the form of a higher version of T-duality in string theory. This involves a new topology change mechanism abelianizing the 3-sphere associated with the C-field topology to the 517-torus associated with exceptional-generalized super-geometry. Finall...

By analyzing super-torsion and brane super-cocycles, we derive a new duality in M-theory, which takes the form of a higher version of T-duality in string theory. This involves a new topology change mechanism abelianizing the 3-sphere associated with the C-field topology to the 517-torus associated with exceptional-generalized super-geometry. Finall...

Deligne cohomology can be viewed as a differential refinement of integral cohomology, hence captures both topological and geometric information. On the other hand, it can be viewed as the simplest nontrivial version of a differential cohomology theory. While more involved differential cohomology theories have been explicitly twisted, the same has n...

We establish a higher generalization of super L-infinity-algebraic T-duality of super WZW-terms for super p-branes. In particular, we demonstrate spherical T-duality of super M5-branes propagating on exceptional-geometric 11d super spacetime.

Degree one twisting of Deligne cohomology, as a differential refinement of integral cohomology, was established in previous work. Here we consider higher degree twists. The Rham complex, hence de Rham cohomology, admits twists of any odd degree. However, in order to consider twists of integral cohomology we need a periodic version. Combining the pe...

We combine Sullivan models from rational homotopy theory with Stasheff's $L_\infty$-algebras to describe a duality in string theory. Namely, what in string theory is known as topological T-duality between $K^0$-cocycles in type IIA string theory and $K^1$-cocycles in type IIB string theory, or as Hori's formula, can be recognized as a Fourier-Mukai...

We construct the Atiyah-Hirzebruch spectral sequence (AHSS) for twisted differential generalized cohomology theories. This generalizes to the twisted setting the authors' corresponding earlier construction for differential cohomology theories, as well as to the differential setting the AHSS for twisted generalized cohomology theories, including tha...

Twisted Morava K-theory, along with computational techniques, including a universal coefficient theorem and an Atiyah-Hirzebruch spectral sequence, was introduced by Craig Westerland and the first author. We employ these techniques to compute twisted Morava K-theory of all connective covers of the stable orthogonal group and stable unitary group, a...

We develop a theory of parametrized geometric cobordism by introducing smooth Thom stacks. This requires identifying and constructing a smooth representative of the Thom functor acting on vector bundles equipped with extra geometric data, leading to a geometric refinement of the the Pontrjagin-Thom construction in stacks. We demonstrate that the re...

Deligne cohomology can be viewed as a differential refinement of integral cohomology, hence captures both topological and geometric information. On the other hand, it can be viewed as the simplest nontrivial version of a differential cohomology theory. While more involved differential cohomology theories have been explicitly twisted, the same has n...

The study of higher tangential structures, arising from higher connected covers of Lie groups (String, Fivebrane, Ninebrane structures), require considerable machinery for a full description, especially for connections to geometry and applications. With utility in mind, in this paper we study these structures at the rational level and by considerin...

We compute the $L_\infty$-theoretic dimensional reduction of the F1/D$p$-brane super $L_\infty$-cocycles with coefficients in rationalized twisted K-theory from the 10d type IIA and type IIB super Lie algebras down to 9d. We show that the two resulting coefficient $L_\infty$-algebras are naturally related by an $L_\infty$-isomorphism which we find...

We show that supercocycles on super $L_\infty$-algebras capture, at the rational level, the twisted cohomological charge structure of the fields of M-theory and of type IIA string theory. We show that rational 4-sphere-valued supercocycles for M-branes in M-theory descend to supercocycles in type IIA string theory to yield the Ramond-Ramond fields...

We consider spectral sequences in smooth generalized cohomology theories, including differential generalized cohomology theories. The main differential spectral sequences will be of the Atiyah-Hirzebruch (AHSS) type, where we provide a filtration by the Cech resolution of smooth manifolds. This allows for systematic study of torsion in differential...

We characterize primary operations in differential cohomology via stacks, and illustrate by differentially refining Steenrod squares and Steenrod powers explicitly. This requires a delicate interplay between integral, rational, and mod p cohomology, as well as cohomology with U(1) coefficients and differential forms. Along the way we develop comput...

We introduce a periodic form of the iterated algebraic K-theory of ku, the (connective) complex K-theory spectrum, as well as a natural twisting of this cohomology theory by higher gerbes. Furthermore, we prove a form of topological T-duality for sphere bundles oriented with respect to this theory.

We extend Massey products from cohomology to differential cohomology via
stacks, organizing and generalizing existing constructions in Deligne
cohomology. We study the properties and show how they are related to more
classical Massey products in de Rham, singular, and Deligne cohomology. The
setting and the algebraic machinery via stacks allow for...

We uncover higher algebraic structures on Noether currents and BPS charges.
It is known that equivalence classes of conserved currents form a Lie algebra.
We show that at least for target space symmetries of higher parameterized
WZW-type sigma-models this naturally lifts to a Lie (p+1)-algebra structure on
the Noether currents themselves. Applied t...

We combine rational homotopy theory and higher Lie theory to describe the Wess-Zumino-Witten (WZW) term in the M5-brane sigma model. We observe that this term admits a natural interpretation as a twisted 7-cocycle on super-Minkowski spacetime with coefficients in the rational 4-sphere. This exhibits the WZW term as an element in twisted cohomology,...

String structures have played an important role in algebraic topology, via
elliptic genera and elliptic cohomology, in differential geometry, via the
study of higher geometric structures, and in physics, via partition functions.
We extend the description of String structures from connected covers of the
definite-signature orthogonal group ${\rm O}(...

For G = G(ℝ), a split, simply connected, semisimple Lie group of rank n and K the maximal compact subgroup of G, we give a method for computing Iwasawa coordinates of K∖G using the Chevalley generators and the Steinberg presentation. When K∖G is a scalar coset for a supergravity theory in dimensions ≥3, we determine the action of the integral form...

String structures in degree four are associated with cancellation of
anomalies of string theory in ten dimensions. Fivebrane structures in degree
eight have recently been shown to be associated with cancellation of anomalies
associated to the NS5-brane in string theory as well as the M5-brane in
M-theory. We introduce and describe "Ninebrane struct...

We enhance the action of higher abelian gauge theory associated to a gerbe on
an M5-brane with an action of a torus T^n (n>1), by a noncommutative
T^n-deformation of the M5-brane, showing that the partition function associated
to this enhanced action is a modular form, which is a purely noncommutative
geometry phenomenon since the usual theory only...

We uncover and highlight relations between the M-branes in M-theory and
various topological invariants: the Hopf invariant over Q, Z and Z_2, the
Kervaire invariant, the f-invariant, and the nu-invariant. This requires either
a framing or a corner structure. The canonical framing provides a minimum for
the classical action and the change of framing...

We formalize higher dimensional and higher gauge WZW-type sigma-model local
prequantum field theory, and discuss its rationalized/perturbative description
in (super-)Lie n-algebra homotopy theory (the true home of the "FDA"-language
used in the supergravity literature). We show generally how the intersection
laws for such higher WZW-type sigma-mode...

The first part of this text is a gentle exposition of some basic
constructions and results in the extended prequantum theory of
Chern-Simons-type gauge field theories. We explain in some detail how the
action functional of ordinary 3d Chern-Simons theory is naturally localized
("extended", "multi-tiered") to a map on the universal moduli stack of
p...

The proper action functional of (4k+3)-dimensional U(1)-Chern-Simons theory
including the instanton sectors has a well known description: it is given on
the moduli space of fields by the fiber integration of the cup product square
of classes in degree-(2k+2) differential cohomology. We first refine this
statement from the moduli space to the full h...

We study the effects of having multiple Spin structures on the partition
function of the spacetime fields in M-theory. This leads to a potential
anomaly which appears in the eta invariants upon variation of the Spin
structure. The main sources of such spaces are manifolds with nontrivial
fundamental group, which are also important in realistic mode...

The study of the partition function in M-theory involves the use of index
theory on a twelve-dimensional bounding manifold. In eleven dimensions, viewed
as a boundary, this is given by secondary index invariants such as the
Atiyah-Patodi-Singer eta-invariant, the Chern-Simons invariant, or the Adams
e-invariant. If the eleven-dimensional manifold i...

The higher gauge field in 11-dimensional supergravity—the C-field—is constrained by quantum effects to be a cocycle in some twisted version of differential cohomology. We argue that it should indeed be a cocycle in a certain twisted nonabelian differential cohomology. We give a simple and natural characterization of the full smooth moduli 3-stack o...

The worldvolume theory of coincident M5-branes is expected to contain a
nonabelian 2-form/nonabelian gerbe gauge theory that is a higher analog of
self-dual Yang-Mills theory. But the precise details -- in particular the
global moduli / instanton / magnetic charge structure -- have remained elusive.
Here we deduce from anomaly cancellation a natura...

To study topological aspects of the partition function of the NS5-brane in
type IIA string theory, we define a cohomology class whose vanishing is a
necessary condition for this function to be well-defined. This leads to various
topological conditions, including a twisted Fivebrane structure as well as
secondary cohomology operations arising from a...

We study global gravitational anomalies in type IIB string theory with
nontrivial middle cohomology. This requires the study of the action of
diffeomorphisms on this group. Several results and constructions, including
some recent vanishing results via elliptic genera, make it possible to consider
this problem. Along the way, we describe in detail t...

Studying the topological aspects of M-branes in M-theory leads to various
structures related to Wu classes. First we interpret Wu classes themselves as
twisted classes and then define twisted notions of Wu structures. These
generalize many known structures, including Pin^- structures, twisted Spin
structures in the sense of Distler-Freed-Moore, Wu-...

For an integral cohomology class H of degree n+2 on a space X, we define
twisted Morava K-theory K(n)(X; H) at the prime 2, as well as an integral
analogue. We explore properties of this twisted cohomology theory, study a
twisted Atiyah-Hirzebruch spectral sequence, and give a universal coefficient
theorem (in the spirit of Khorami). We extend the...

Recent years have seen noteworthy progress in the mathematical formulation of
quantum field theory and perturbative string theory. We give a brief survey of
these developments. It serves as an introduction to the more detailed
collection "Mathematical Foundations of Quantum Field Theory and Perturbative
String Theory".

We interpret heterotic M-theory in terms of h-cobordism, that is the
eleven-manifold is a product of the ten-manifold times an interval is
translated into a statement that the former is a cobordism of the latter which
is a homtopy equivalence. In the non-simply connected case, which is important
for model building, the interpretation is then in ter...

The actions, anomalies, and quantization conditions allow the M2-brane and
the M5-brane to support, in a natural way, structures beyond Spin on their
worldvolumes. The main examples are twisted String structures. This also
extends to twisted String^c structures, which we introduce and relate to
twisted String structures. The relation of the C-field...

M-theory can be defined on closed manifolds as well as on manifolds with
boundary. As an extension, we show that manifolds with corners appear naturally
in M-theory. We illustrate this with four situations: The lift to bounding
twelve dimensions of M-theory on Anti de Sitter spaces, ten-dimensional
heterotic string theory in relation to twelve dime...

We consider geometric and analytical aspects of M-theory on a manifold with
boundary Y. The partition function of the C-field requires summing over
harmonic forms. When Y is closed Hodge theory gives a unique harmonic form in
each de Rham cohomology class, while in the presence of a boundary the
Hodge-Morrey-Friedrichs decomposition should be used....

The equations of motion and the Bianchi identity of the C-field in M-theory
are encoded in terms of the signature operator. We then reformulate the
topological part of the action in M-theory using the signature, which leads to
connections to the geometry of the underlying manifold, including positive
scalar curvature. This results in a variation on...

Studying the M-branes leads us naturally to new structures that we call
Membrane-, Membrane^c-, String^K(Z,3)- and Fivebrane^K(Z,4)-structures, which
we show can also have twisted counterparts. We study some of their basic
properties, highlight analogies with structures associated with lower levels of
the Whitehead tower of the orthogonal group, an...

The adjoint representations of the Lie algebras of the classical groups SU(n), SO(n), and Sp(n) are, respectively, tensor, antisymmetric, and symmetric products of two vector spaces, and hence are matrix representations. We consider the analogous products of three vector spaces and study when they appear as summands in Lie algebra decompositions. T...

We consider the topological and geometric structures associated with cohomological and homological objects in M-theory. For the latter, we have M2-branes and M5-branes, the analysis of which requires the underlying spacetime to admit a String structure and a Fivebrane structure, respectively. For the former, we study how the fields in M-theory are...

The reduction of the $E_8$ gauge theory to ten dimensions leads to a loop
group, which in relation to twisted $K$-theory has a Dixmier–Douady class
identified with the Neveu–Schwarz $H$-field. We give an interpretation of
the degree two part of the eta form by comparing the adiabatic limit of the
eta invariant with the one loop term in type IIA. Mo...

In the background effective field theory of heterotic string theory, the Green-Schwarz anomaly cancellation mechanism plays a key role. Here we reinterpret it and its magnetic dual version in terms of, differential twisted String- and differential twisted Fivebrane-structures that generalize the notion of Spin-structures and Spin-lifting gerbes and...

The massless supermultiplet of eleven-dimensional supergravity can be
generated from the decomposition of certain representation of the exceptional
Lie group F4 into those of its maximal compact subgroup Spin(9). In an earlier
paper, a dynamical Kaluza-Klein origin of this observation is proposed with
internal space the Cayley plane, OP2, and topol...

Considering the gauge field and its dual in heterotic string theory as a unified field, we show that the equations of motion at the rational level contain a twisted differential with a novel degree seven twist. This generalizes the usual degree three twist that lifts to twisted K-theory and raises the natural question of whether at the integral lev...

Ramond has observed that the massless multiplet of eleven-dimensional supergravity can be generated from the decomposition of certain representation of the exceptional Lie group F4 into those of its maximal compact subgroup Spin(9). The possibility of a topological origin for this observation is investigated by studying Cayley plane, OP2, bundles o...

In this note we revisit the subject of anomaly cancelation in string theory
and M-theory on manifolds with String structure and give three observations.
First, that on String manifolds there is no E8 x E8 global anomaly in heterotic
string theory. Second, that the description of the anomaly in the phase of the
M-theory partition function of Diacone...

We study the cohomological physics of fivebranes in type II and heterotic string theory. We give an interpretation of the one-loop term in type IIA, which involves the first and second Pontrjagin classes of spacetime, in terms of obstructions to having bundles with certain structure groups. Using a generalization of the Green-Schwarz anomaly cancel...

The M-theory field strength and its dual, given by the integral lift of the left-hand side of the equation of motion, both satisfy certain cohomological properties. We study the combined fields and observe that the multiplicative structure on the product of the corresponding degree four and degree eight cohomology fits into that given by Spin K-the...

We give a generalization of the notion of a Cartan-Ehresmann connection from Lie algebras to L∞algebras and use it to study the obstruction theory of lifts through higher String-like extensions of Lie algebras. It is known that over a D-brane the Kalb-Ramond background field of the string restricts to a 2-bundle with connection (a gerbe) which can...