[Show abstract][Hide abstract]ABSTRACT: In this paper we study the low energy physics of Landau-Ginzburg models with N=(0,2) supersymmetry. We exhibit a number of classes of relatively simple LG models where the conformal field theory at the low energy fixed point can be explicitly identified. One interesting class of fixed points can be thought of as "heterotic" minimal models. Other examples include N=(0,2) renormalization group flows that end up at N=(2,2) minimal models and models with non-abelian symmetry.
[Show abstract][Hide abstract]ABSTRACT: In this paper we study the constraints imposed by conformal invariance on extended objects a.k.a defects in a conformal field theory. We identify a particularly nice class of defects that is closed under conformal transformations. Correlation function of the defect with a bulk local operator is fixed by conformal invariance up to an overall constant. This gives rise to the notion of defect expansion, where the defect itself is expanded in terms of local operators. This expansion generalizes the idea of the boundary state. We will show how one can fix the correlation function of two defects from the knowledge of the defect expansion. The defect correlator admits a number of conformal cross-ratios depending on their dimensionality. We find the differential equation obeyed by the conformal block and solve them in certain special cases.
[Show abstract][Hide abstract]ABSTRACT: We describe rules for building 2d theories labeled by 4-manifolds. Using the proposed dictionary between building blocks of 4-manifolds and 2d \(\mathcal{N} = (0,2)\) theories, we obtain a number of results, which include new 3d \(\mathcal{N} = 2\) theories T[M
3] associated with rational homology spheres and new results for Vafa–Witten partition functions on 4-manifolds. In particular, we point out that the gluing measure for the latter is precisely the superconformal index of 2d (0, 2) vector multiplet and relate the basic building blocks with coset branching functions. We also offer a new look at the fusion of defect lines/walls, and a physical interpretation of the 4d and 3d Kirby calculus as dualities of 2d \(\mathcal{N} = (0,2)\) theories and 3d \(\mathcal{N} = 2\) theories, respectively.
[Show abstract][Hide abstract]ABSTRACT: We discuss reductions of general \( \mathcal{N}=1 \) four dimensional gauge theories on \( {\mathbb{S}}^2 \). The effective two dimensional theory one obtains depends on the details of the coupling of the theory to background fields, which can be translated to a choice of R-symmetry. We argue that, for special choices of R-symmetry, the resulting two dimensional theory has a natural interpretation as an \( \mathcal{N}=\left(0,2\right) \) gauge theory. As an application of our general observations, we discuss reductions of \( \mathcal{N}=1 \) and \( \mathcal{N}=2 \) dualities and argue that they imply certain two dimensional dualities.
Article · Nov 2015 · Journal of High Energy Physics
[Show abstract][Hide abstract]ABSTRACT: We discuss reductions of general N=1 four dimensional gauge theories on S^2.
The effective two dimensional theory one obtains depends on the details of the
coupling of the theory to background fields, which can be translated to a
choice of R-symmetry. We argue that, for special choices of R-symmetry, the
resulting two dimensional theory has a natural interpretation as an N=(0,2)
gauge theory. As an application of our general observations, we discuss
reductions of N=1 and N=2 dualities and argue that they imply certain two
dimensional dualities.
[Show abstract][Hide abstract]ABSTRACT: We suggest an N=1 Lagrangian flowing in the infra-red to the N=2 rank one
superconformal field theory with E_6 flavor symmetry. We utilize this
description to compute several supersymmetric partition functions.
[Show abstract][Hide abstract]ABSTRACT: We consider bound states of strings which arise in 6d (1,0) SCFTs that are
realized in F-theory in terms of linear chains of spheres with negative
self-intersections 1,2, and 4. These include the strings associated to N small
E8 instantons, as well as the ones associated to M5 branes probing A and D type
singularities in M-theory or D5 branes probing ADE singularities in Type IIB
string theory. We find that these bound states of strings admit (0,4)
supersymmetric quiver descriptions and show how one can compute their elliptic
genera.
[Show abstract][Hide abstract]ABSTRACT: We study dynamics of two-dimensional non-abelian gauge theories with N=(0,2)
supersymmetry that include N=(0,2) supersymmetric QCD and its generalizations.
In particular, we present the phase diagram of N=(0,2) SQCD and determine its
massive and low-energy spectrum. We find that the theory has no mass gap, a
nearly constant distribution of massive states, and lots of massless states
that in general flow to an interacting CFT. For a range of parameters where
supersymmetry is not dynamically broken at low energies, we give a complete
description of the low-energy physics in terms of 2d N=(0,2) SCFTs using
anomaly matching and modular invariance. Our construction provides a vast
landscape of new N=(0,2) SCFTs which, for small values of the central charge,
could be used for building novel heterotic models with no moduli and, for large
values of the central charge, could be dual to AdS_3 string vacua.
[Show abstract][Hide abstract]ABSTRACT: We propose a unified approach to a general class of codimension-2 defects in
field theories with non-trivial duality symmetries and discuss various
constructions of such "duality defects" in diverse dimensions. In particular,
in d=4 we propose a new interpretation of the Seiberg-Witten u-plane by
"embedding" it in the physical space-time: we argue that it describes a BPS
configuration of two duality defects (at the monopole/dyon points) and propose
its vast generalization based on Lefschetz fibrations of 4-manifolds.
[Show abstract][Hide abstract]ABSTRACT: We investigate the superconformal index of four-dimensional superconformal field theories that arise on coincident M5 branes wrapping a holomorphic curve in a local Calabi-Yau three-fold. The structure of the index is very similar to that which appears in the special case preserving = 2 supersymmetry. We first compute the index for the fixed points that admit a known four-dimensional ultraviolet description and prove infrared equivalence at the level of the index for all such constructions. These results suggest a formulation of the index as a two-dimensional topological quantum field theory that generalizes the one that computes the = 2 index. The TQFT structure leads to an expression for the index of a much larger family of = 1 class S fixed points in terms of the index of the = 2 theories. Calculations of simple quantities with the index suggests a connection between these families of fixed points and the mathematics of SU(2) Yang-Mills theory on the wrapped curve.
Article · Mar 2014 · Journal of High Energy Physics
[Show abstract][Hide abstract]ABSTRACT: Motivated by the connection between 4-manifolds and 2d N = (0, 2) theories,
we study the dynamics of a fairly large class of 2d N = (0, 2) gauge theories. We see that
physics of such theories is very rich, much as the physics of 4d N = 1 theories. We discover
a new type of duality that is very reminiscent of the 4d Seiberg duality. Surprisingly, the
new 2d duality is an operation of order three: it is IR equivalence of three different theories
and, as such, is actually a triality. We also consider quiver theories and study their triality
webs. Given a quiver graph, we find that supersymmetry is dynamically broken unless the
ranks of the gauge groups and flavor groups satisfy stringent inequalities. In fact, for most
of the graphs these inequalities have no solutions. This supports the folklore theorem that
generic 2d N = (0, 2) theories break supersymmetry dynamically.
Article · Feb 2014 · Journal of High Energy Physics
[Show abstract][Hide abstract]ABSTRACT: Motivated by the connection between 4-manifolds and 2d N=(0,2) theories, we
study the dynamics of a fairly large class of 2d N=(0,2) gauge theories. We see
that physics of such theories is very rich, much as the physics of 4d N=1
theories. We discover a new type of duality that is very reminiscent of the 4d
Seiberg duality. Surprisingly, the new 2d duality is an operation of order
three: it is IR equivalence of three different theories and, as such, is
actually a triality. We also consider quiver theories and study their triality
webs. Given a quiver graph, we find that supersymmetry is dynamically broken
unless the ranks of the gauge groups and flavor groups satisfy stringent
inequalities. In fact, for most of the graphs these inequalities have no
solutions. This supports the folklore theorem that generic 2d N=(0,2) theories
break supersymmetry dynamically.
[Show abstract][Hide abstract]ABSTRACT: We study the integrability properties of planar \( \mathcal{N}=2 \) superconformal field theories in four dimensions. We show that the spin chain associated to the planar dilation operator of \( \mathcal{N}=2 \) superconformal QCD fails to be integrable at two loops. In our analysis we focus on a closed SU(2|1) sector, whose two-loop spin chain we fix by symmetry arguments (up to a few undetermined coefficients). It turns out that the Yang-Baxter equation for magnon scattering is not satisfied in this sector. On the other hand, we suggest that the closed SU(2, 1|2) sector, which exists in any \( \mathcal{N}=2 \) superconformal gauge theory, may be integrable to all loops. We summarize the known results in the literature that are consistent with this conjecture.
Article · Aug 2013 · Journal of High Energy Physics
[Show abstract][Hide abstract]ABSTRACT: We describe rules for building 2d theories labeled by 4-manifolds. Using the
proposed dictionary between building blocks of 4-manifolds and 2d N=(0,2)
theories, we obtain a number of results, which include new 3d N=2 theories
T[M_3] associated with rational homology spheres and new results for
Vafa-Witten partition functions on 4-manifolds. In particular, we point out
that the gluing measure for the latter is precisely the superconformal index of
2d (0,2) vector multiplet and relate the basic building blocks with coset
branching functions. We also offer a new look at the fusion of defect lines /
walls, and a physical interpretation of the 4d and 3d Kirby calculus as
dualities of 2d N=(0,2) theories and 3d N=2 theories, respectively
[Show abstract][Hide abstract]ABSTRACT: We show that the N=1 supersymmetric SU(N) gauge theory with 2N flavors without superpotential has not only the standard Seiberg dual description but also another dual description involving two copies of the so-called T_N theory. This is a natural generalization to N > 2 of a dual description of SU(2) gauge theory with 4 flavors found by Csaki, Schmaltz, Skiba and Terning. We also study dualities of other N=1 SCFTs involving copies of T_N theories. Our duality is the basic operation from which a recently-found web of N=1 dualities obtained by compactifying M5-branes on Riemann surfaces can be derived field-theoretically.
Article · Jun 2013 · Journal of High Energy Physics
[Show abstract][Hide abstract]ABSTRACT: We show that the
$ \mathcal{N} $
=1 supersymmetric SU(N) gauge theory with 2N flavors without superpotential has not only the standard Seiberg dual description but also another dual description involving two copies of the so-called T
N
theory. This is a natural generalization to N > 2 of a dual description of SU(2) gauge theory with 4 flavors found by Csaki, Schmaltz, Skiba and Terning. We also study dualities of other
$ \mathcal{N} $
=1 SCFTs involving copies of T
N
theories. Our duality is the basic operation from which a recently-found web of
$ \mathcal{N} $
=1 dualities obtained by compactifying M5-branes on Riemann surfaces can be derived field-theoretically.
Article · Jun 2013 · Journal of High Energy Physics
[Show abstract][Hide abstract]ABSTRACT: In this paper we compute the superconformal index of 2d (2, 2) supersymmetric gauge theories. The 2d superconformal index, a.k.a. flavored elliptic genus, is computed by a unitary matrix integral much like the matrix integral that computes the 4d superconformal index. We compute the 2d index explicitly for a number of examples. In the case of abelian gauge theories we see that the index is invariant under flop transition and under CY-LG correspondence. The index also provides a powerful check of the Seiberg-type duality for non-abelian gauge theories discovered by Hori and Tong.
In the later half of the paper, we study half-BPS surface operators in \( \mathcal{N} \) = 2 super-conformal gauge theories. They are engineered by coupling the 2d (2, 2) supersymmetric gauge theory living on the support of the surface operator to the 4d \( \mathcal{N} \) = 2 theory, so that different realizations of the same surface operator with a given Levi type are related by a 2d analogue of the Seiberg duality. The index of this coupled system is computed by using the tools developed in the first half of the paper. The superconformal index in the presence of surface defect is expected to be invariant under generalized S-duality. We demonstrate that it is indeed the case. In doing so the Seiberg-type duality of the 2d theory plays an important role.
Article · May 2013 · Journal of High Energy Physics
[Show abstract][Hide abstract]ABSTRACT: In this paper we analyze various half-BPS defects in a general three
dimensional N=2 supersymmetric gauge theory T. They correspond to closed paths
in SUSY parameter space and their tension is computed by evaluating period
integrals along these paths. In addition to such defects, we also study wall
defects that interpolate between T and its SL(2,Z) transform by coupling the 3d
theory to a 4d theory with S-duality wall. We propose a novel spectral duality
between 3d gauge theories and integrable systems. This duality complements a
similar duality discovered by Nekrasov and Shatashvili. As another application,
for 3d N=2 theories associated with knots and 3-manifolds we compute periods of
(super) A-polynomial curves and relate the results with the spectrum of domain
walls and line operators.
Article · Jan 2013 · Journal of High Energy Physics
[Show abstract][Hide abstract]ABSTRACT: We investigate the superconformal index of four-dimensional N=1
superconformal field theories that arise on coincident M5 branes wrapping a
holomorphic curve in a local Calabi-Yau three-fold. The structure of the index
is very similar to that which appears in the special case preserving N=2
supersymmetry. We first compute the index for the fixed points that admit a
known four-dimensional ultraviolet description and prove infrared equivalence
at the level of the index for all such constructions. These results suggest a
formulation of the index as a two-dimensional topological quantum field theory
that generalizes the one that computes the N=2 index. The TQFT structure leads
to an expression for the index of all class S fixed points in terms of the
index of the N=2 theories. Calculations of spectral data using the index
suggests a connection between these families of fixed points and the
mathematics of SU(2) Yang-Mills theory on the wrapped curve.
[Show abstract][Hide abstract]ABSTRACT: We study the integrability properties of planar N=2 superconformal field
theories in four dimensions. We show that the spin chain associated to the
planar dilation operator of N=2 superconformal QCD fails to be integrable at
two loops. In our analysis we focus on a closed SU(2|1) sector, whose two-loop
spin chain we fix by symmetry arguments (up to a few undetermined
coefficients). It turns out that the Yang-Baxter equation for magnon scattering
is not satisfied in this sector. On the other hand, we suggest that the closed
SU(2,1|2) sector, which exists in any N=2 superconformal gauge theory, may be
integrable to all loops.