Carsten Lutken

University of Oslo · Department of Physics

Toroidal sigma models of magneto-transport are analyzed, in which integer and fractional quantum Hall effects automatically are unified by a holomorphic modular symmetry, whose group structure is determined by the spin structure of the toroidal target space (an elliptic curve). Hall quantization is protected by the topology of stable holomorphic ve...

We analyze experimental quantum Hall data from a wide range of different materials, including semiconducting heterojunctions, thin films, surface layers, graphene, mercury telluride, bismuth antimonide, and black phosphorus. The fact that these materials have little in common, except that charge transport is effectively two-dimensional, shows how r...

An introduction to the theory of modular symmetries in two-dimensional materials, and its application to ‘relativistic’ group IV materials like graphene, silicene, germanene and stanene, is given. Universal properties of the magneto-electric Hall effect are extracted by projecting experimental transport data directly onto the phase diagram. When fa...

The new states of matter and concomitant quantum critical phenomena revealed by the quantum Hall effect appear to be accompanied by an emergent modular symmetry. The extreme rigidity of this infinite symmetry makes it easy to falsify, but two decades of experiments have failed to do so, and the location of quantum critical points predicted by the s...

We investigate a finite size “double scaling” hypothesis using data from an experiment on a quantum Hall system with short range disorder [1-3]. For Hall bars of width w at temperature T the scaling form is wT, where the critical exponent μ≈0.23 we extract from the data is comparable to the multi-fractal exponent α0-2 obtained from the Chalker-Codd...

We show how the modular symmetries that have been found to be consistent with most available scaling data from quantum Hall systems, derive from a rigid family of algebraic curves of the elliptic type. The complicated special functions needed to describe scaling data arise in a simple and transparent way from the group theory and geometry of these...

The phenomenological analysis of fully spin-polarized quantum Hall systems, based on holomorphic modular symmetries of the renormalization group (RG) flow, is generalized to more complicated situations where the spin or other “flavors” of charge carriers are relevant, and where the symmetry is different. We make the simplest possible ansatz for a f...

Universitetet i Oslo: UNIPUB 2012 40 s.

A second quantized formalism for electrons confined to a plane in a strong perpendicular magnetic field is constructed using vertex operators. They are seen to arise naturally from a holomorphic representation of Laughlin’s first quantized wave functions, since they have the unique properties of creating coherent states, satisfying anyonic statisti...

We show that some of the nonlinear conductance properties of electro-osmosis in sweat-duct capillaries may be modeled by a memristive circuit. This includes both the observed phase shift and amplitude modulation of the electrical current response to a simple harmonic driving potential. Memristive sytems may therefore be expected to play a role in m...

Experiments studying renormalization group flows in the quantum Hall system provide significant evidence for the existence of an emergent holomorphic modular symmetry $\Gamma_0(2)$. We briefly review this evidence and show that, for the lowest temperatures, the experimental determination of the position of the quantum critical points agrees to the...

We discuss the possible origin of the duality observed in the quantum Hall current-voltage characteristics. We clarify the difference between "particle-vortex" (complex modular) duality, which acts on the full transport tensor, and "charge-flux" ("real") duality, which acts directly on the filling factor. Comparison with experiment strongly favors...

The memristor is basically a resistor with memory, so that the resistance is dependent on the net amount of charge having passed through the device. It is the regarded the fourth fundamental component, in addition to the resistor, capacitor and inductor, that can be deduced from the four basic circuit variables; current, voltage, charge and magneti...

The memristor was predicted to exist on purely theoretical grounds many years ago, but was not realized in the laboratory as a physical, electronic nano-component until last year. We show that electro-osmosis in human sweat ducts is of memristive nature and that memristors therefore will be important when modeling electrical properties of human ski...

We review the implications of the scaling data for the emergent symmetry of the quantum Hall system. The location of the fixed points in the conductivity plane is consistent with the global, non-Abelian discrete symmetry $\Gamma _{0}(2)$, and the renormalisation group (RG) flow-lines agree closely with that found if the symmetry acts anti-holomorph...

The transitions between neighbouring plateaux in the quantum Hall system are observed to follow anti-holomophic scaling with superuniversal scaling exponents, showing that the system contains an emergent sub-modular discrete symmetry and a holomorphic structure at low energies. We identify a class of effective scaling models consistent with this da...

The vacuum fluctuations of the electric field will shift the energy levels of an atom near a neutral, conducting plate. We have calculated these shifts in Rydberg atoms. The results of Casimir and Polder are recovered in the limit where one ignores any permanent dipole moment in the atom. Numerical values for the shifts of the lowest levels are giv...

Experimental and theoretical evidence which is accumulating in favor of the existence of a global sub-modular symmetry in the quantum Hall system is reviewed. The scaling data suggest that the zeros of the beta-function are effectively anti-holomorphic, and it is explained how this leads to a superuniversal scaling function. This motivates the firs...

We point out that scaling data strongly suggest that the zeros of the beta-function for the quantum Hall system are effectively anti-holomorphic. All scaling data, both experimental and numerical, are accounted for if the quantum Hall conductivities scale as the unique anti-holomorphic function automorphic under the complexified duality group Gamma...

We explore entanglement loss along renormalization group trajectories as a basic quantum information property underlying their irreversibility. This analysis is carried out for the quantum Ising chain as a transverse magnetic field is changed. We consider the ground-state entanglement between a large block of spins and the rest of the chain. Entang...

We show that B-type Π-stable D-branes do not in general reduce to the (Gieseker-) stable holomorphic vector bundles used in mathematics to construct moduli spaces. We show that solutions of the almost Hermitian Yang–Mills equations for the non-linear deformations of Yang–Mills instantons that appear in the low-energy geometric limit of strings exis...

We show that B-type $\Pi$-stable D-branes do not in general reduce to the (Gieseker-) stable holomorphic vector bundles used in mathematics to construct moduli spaces. We show that solutions of the almost Hermitian Yang--Mills equations for the non-linear deformations of Yang--Mills instantons that appear in the low-energy geometric limit of string...

We investigate certain fixed points in the boundary conformal field theory representation of type IIA D-branes on Gepner points of K3. They correspond geometrically to degenerate brane configurations, and physically lead to enhanced gauge symmetries on the world-volume. Non-abelian gauge groups arise if the stabilizer group of the fixed points is r...

B-type D-branes are constructed on two different K3-fibrations over using boundary conformal field theory at the rational Gepner points of these models. The microscopic CFT charges are compared with the Ramond charges of D-branes wrapped on holomorphic cycles of the corresponding Calabi–Yau manifold. We study in particular D4-branes and bundles loc...

The spectrum of D2-branes wrapped on an ALE space of general ADE type is determined, by representing them as boundary states of superconformal minimal models. The stable quantum states have RR charges which precisely represent the gauge fields of the corresponding Lie algebra. This provides a simple and direct physical link between the ADE classifi...

B-type D-branes are constructed on two different K3-fibrations over IP_1 using boundary conformal field theory at the rational Gepner points of these models. The microscopic CFT charges are compared with the Ramond charges of D-branes wrapped on holomorphic cycles of the corresponding Calabi-Yau manifold. We study in particular D4-branes and bundle...

We argue that the large discrete symmetry group of quantum Hall systems is insufficient in itself to determine the complete beta function for the scaling of the conductivities, $\sigma_{xx}$ and $\sigma_{xy}$. We illustrate this point by showing that a recent ansatz for this function is one of a many-parameter family. A clean prediction for the del...

Vacuum fluctuations at finite temperature between two plane walls give rise to a Casimir energy which has a simple symmetry between high and low temperatures. This symmetry is most easily understood in a derivation based on functional methods using dimensional regularisation and generalised zeta functions.

As a primitive model of spontaneous breakdown of chiral symmetry for strongly interacting quarks, the authors have considered confined fermions between parallel plates. The massless fermion field satisfies the chiral MIT boundary condition. Explicit expressions for the fermion condensate ( psi psi ) and the vacuum expectation value of the energy-mo...

The authors compute explicitly all the Hodge numbers for all Calabi-Yau manifolds realised as complete intersections of hypersurfaces in products of complex projective spaces. This determines the essential part of the matter superfield spectrum for the heterotic superstring compactified on any of these manifolds. They use various techniques present...

The authors calculate the effective potential for the bosonic sector of eleven-dimensional supergravity on the background (Minkowski)*(sphere). They find no tachyons and show that the antisymmetric tensor field does not threaten graviton dominance when the Freund-Rubin parameter (m) vanishes. The general cases (m not=0) seems intractable in the pre...

The author computes the normalisation matrix and Yukawa couplings on the Z-manifold in the geometric approximation where the singularities on the Z-orbifold are blown up with Eguchi-Hanson metrics (1980). The orbifold limit is discussed in detail from a geometric and algebraic point of view, and the results are compared with those obtained using al...

The authors calculate the effective potential for gravitinos in eleven-dimensional supergravity on the background (Minkowski)*S7. As in the case of pure gravity the potential is unexpectedly large compared with the results previously obtained for lower spin fields. However, the gravitino contribution to the vacuum energy is still much smaller than...

It is suggested that it is not necessary to solve the full non-perturbative problem of two-dimensional charge transport in order to obtain global information about the phase and flow diagrams for the quantum Hall system and its relatives. It is argued that the effective quantum field theories encoding the macroscopic properties of these systems are...

It has been proposed that the effective Hamiltonian describing high T_c superconductivity in cuprate materials has an approximate SO(5) symmetry relating the superconducting (SC) and antiferromagnetic (AF) phases of these systems. We show that robust consequences of this proposal are potentially large optical conductivities and Raman scattering rat...

We construct an RG potential for N=2 supersymmetric SU(2) Yang-Mills theory, and extract a positive definite metric by comparing its gradient with the recently discovered beta-function for this system, thus proving that the RG flow is gradient in this four-dimensional field theory. We also discuss how this flow might change after supersymmetry brea...

We set up the effective field theories which describe the SO(5)-invariant picture of the high-Tc cuprates in various regimes. We use these to get quantitative conclusions concerning the size of SO(5)-breaking effects. We consider two applications in detail: (i) the thermodynamic free energy, which describe the phase diagram and critical behaviour,...

We construct the low-energy effective theory for the SO(5) model of high-T_c superconductivity, recently proposed by S.C. Zhang (cond-mat/9610140). This permits us to develop a systematic expansion for low-energy observables in powers of the small symmetry-breaking interactions. The approximate SO(5) symmetry predicts relations amongst these observ...

We construct the c-function whose gradient determines the RG flow of the conductivities (sigma_xy and sigma_xx) for a quantum Hall system, subject to two assumptions. (1) We take the flow to be invariant with respect to the infinite discrete symmetry group, recently proposed by several workers to explain the `superuniversality' of the delocalizatio...

Charge transport in two dimensions provides an ideal laboratory for investigating parameter space geometries. The Onsager relations for anisotropic transport in a parity-violating external field endow these spaces with a highly nontrivial complex (and Khler) structure, which can be given a simple geometrical interpretation. A large class of Coulomb...

We study localization of electrons moving in two dimensions in a smoothly varying potential and a strong perpendicular magnetic field. Classically, the localization-delocalization transition in this system is a percolation transition. However, tunneling changes the universality class of this transition. Using the semiclassical approximation that do...

Using the recently discovered connection between bosonization and duality transformations, we give an explicit path- integral representation for the bosonization of a massive fermion coupled to a U(1) gauge potential (such as electromagnetism) in d ⩾ 2 space (D = d + 1 ⩾ 3 spacetime) dimensions. We perform this integral explicitly in the limit of l...

A discussion of the transport properties of anisotropic Hall samples is presented. Such anisotropic samples can now be made by modulation-doped overgrowth on the cleaved edge of an AlxGa1-xAs compositional superlattice. The central issue here is the structure of the space of transport coefficients. We argue that the geometry and fixed-point structu...

We construct an effective-field theory for the quantum Hall system which embodies both localization and fractional statistics. The latter involves a Chern-Simons interaction, while the former involves a generalization of conventional localization theory. The theory is invariant under ``complexified'' duality transformations of the conductivities wh...

The connection between the phase structure and the geometry of the renormalization group (RG) flow in systems with discrete parameter space symmetries is studied. These are symmetries of the partition function, and therefore determine the geometry of the phase diagram for the system. The C-function, which is the potential for the RG flow, inherits...

We suggest that a unified description of the integer and fractional phases of the quantum Hall system may be possible if the scaling diagram of transport coefficients is invariant under linear fractional (modular) transformations. In this model the hierarchy of states, as well as the observed universality of critical exponents, are consequences of...

We investigate the algebrao-geometric structure which is inherent in 2-dimensional conformally invariant quantum field theories with N=2 supersymmetry, and its relation to the Calabi-Yau manifolds which appear in the so-called “large radius limit”. Based on a careful comparison of the Kähler cone of Calabi-Yau manifolds and the moduli space of marg...

We analyze the mirror manifold hypothesis in one and three dimensions using the simplest available representations of the N = 2 superconformal algebra. The symmetries of these tensor models can be divided out to give an explicit representation of the mirror, and we give a simple group theoretical algorithm for determining which symmetries should be...

We present an analysis of the conjectured existence of Calabi-Yau “mirror manifolds” for the case where the starting manifold is Y4,5. We construct mirror pairs with equal but opposite values for the Euler characteristic and the Hodge numbers h2,1 and h1,1 interchanged. In one particular example we show that the couplings of (1,1)-forms equal the c...

We compute all Yukawa couplings in the three generation string theory recently constructed by Gepner by tensoring solvable N = 2 superconformal theories. The results are consistent with those obtained by a geometric analysis of the field theory limit where the model reduces to a compactification on an algebraic manifold of the Calabi-Yau type.

We construct a large new class of two-dimensional sigma models with Kähler target spaces which are algebraic manifolds realized as complete intersection in weighted CPn spaces. They are N = 2 superconformally symmetric and particular choices of constraints give Calabi-Yau target spaces which are nontrivial string vacua.

ISBN 978-1560720270

From the text: Calabi-Yau manifolds are still the only viable smooth background spaces on which to compactify the heterotic string from ten to four dimensions. The number of such spaces is enormous, but a large ‘core sample’ can be obtained rather easily and analyzed in great detail for possible relevance to phenomenology. They are also useful for...

We discuss the symmetries of the superpotential in comfactified heterotic superstring theories formed from the product of minimal N = 2 superconformal field theories. It is shown how these symmetries can ensure flatness of the potential involving the moduli, and we derive new results (going beyond those obtained by superconformal techniques alone)...

We derive the massless spectrum of all heterotic two-dimensional superconformal field theories constructed by tensoring models from the discrete series (c<3) using diagonal and exceptional affine invariants (but not including the quotients by discrete groups). A comparison is made between these models and known manifold constructions lending some s...

A class of Calabi-Yau spaces of Euler number −6k, for many values of k, is searched to find manifolds which admit a freely acting discrete symmetry group G of order k. For such manifolds one may construct the quotient /G which is a Calabi-Yau manifold of Euler number −6 corresponding to three generations of particles. Surprisingly, we are able to e...

An investigation is made of a class of Calabi-Yau spaces for which the manifold may be represented as a complete intersection of polynomials in a product of projective spaces. There are at least a hundred topologically distinct manifolds in this class. All manifolds in this class have negative Euler numbers which lie in the range of −200 ⩽ χ ⩽0.

The two-point function for spinors on maximally symmetric four-dimensional spaces is obtained in terms of intrinsic geometric objects. In the massless case, Weyl spinors in anti de Sitter space can not satisfy boundary conditions appropriate to the supersymmetric models. This is because these boundary conditions break chiral symmetry, which is prov...

UMI86-18530mc. Austin, Texas: University of Texas at Austin

The vacuum fluctuations of the electric field will shift the energy levels of an atom between two neutral, conducting planes. We have calculated these shifts in hydrogen atoms, and numerical values for the shifts of the lowest levels are given.

We calculate the propagator and one-loop effective potential for a scalar in an n-dimensional anti-de Sitter background. The computation is done by directly summing the modes appropriate to supersymmetric boundary conditions as well as by analytic continuation from the euclidean n-sphere. We show that the direct mode sum gives a physically reasonab...

We investigate certain fixed points in the boundary conformal field theory representation of type IIA D-branes on Gepner points of K3. They correspond geometrically to degenerate brane configurations, and physi- cally lead to enhanced gauge symmetries on the world-volume. Non-abelian gauge groups arise if the stabilizer group of the fixed points is...

The spectrum of D2-branes wrapped on an ALE space of general ADE type is determined, by representing them as boundary states of N = 2 superconformal minimal models. The stable quantum states have RR charges which precisely represent the gauge fields of the corresponding Lie algebra. This provides a simple and direct physical link between the ADE cl...

We review the main idea associated with problems concerning “geometrical” interpretations of the information contained in 2- dimensional N=2 superconformal field theories. At stake is a new way of looking at space-time which is uniquely stringy and which goes a long way towards removing the classical dichotomy between space and matter, thus opening...

Recent scaling experiments have thrown the universality hypothesis for the quantum Hall effect into some confusion. While they appear to con­ fum a novel form of "super-universality" of the delocalization exponent relating transitions between different Landau levels, contrary to expecta­ tion, the experiments have not found universal values for the...