arXiv subjects

I. I. Kogan

Publications and source records attributed to I. I. Kogan.

32 records · Page 2Linked to original sources

arXiv1998

Mirror Maps in Chern-Simons Gauge Theory

We describe mirror symmetry in N=2 superconformal field theories in terms of a dynamical topology changing process of the principal fiber bundle associated with a topological membrane. We show that the topological symmetries of Calabi-Yau sigma-models can be obtained from discrete geometric transformations of compact Chern-Simons gauge theory coupled to charged matter fields. We demonstrate that the appearence of magnetic monopole-instantons, which interpolate between topologically inequivalent vacua of the gauge theory, implies that the discrete symmetry group of the worldsheet theory is realized kinematically in three dimensions as the magnetic flux symmetry group. From this we construct the mirror map and show that it corresponds to the interchange of topologically non-trivial matter field and gauge degrees of freedom. We also apply the mirror transformation to the mean field theory of the quantum Hall effect. We show that it maps the Jain hierarchy into a new hierarchy of states in which the lowest composite fermions have the same filling fractions.

hep-th↗

arXiv1997

Dual Response Models for the Fractional Quantum Hall Effect

It is shown that the Jain mapping between states of integer and fractional quantum Hall systems can be described dynamically as a perturbative renormalization of an effective Chern-Simons field theory. The effects of mirror duality symmetries of toroidally compactified string theory on this system are studied and it is shown that, when the gauge group is compact, the mirror map has the same effect as the Jain map. The extrinsic ingredients of the Jain construction appear naturally as topologically non-trivial field configurations of the compact gauge theory giving a dynamical origin for the Jain hierarchy of fractional quantum Hall states.

cond-mat↗

arXiv1997

Knizhnik-Zamolodchikov-type equations for gauged WZNW models

We study correlation functions of coset constructions by utilizing the method of gauge dressing. As an example we apply this method to the minimal models and to the Witten 2D black hole. We exhibit a striking similarity between the latter and the gravitational dressing. In particular, we look for logarithmic operators in the 2D black hole.

hep-th↗

arXiv1997

D-brane Configurations and Nicolai Map in Supersymmetric Yang-Mills Theory

We discuss some properties of a supersymmetric matrix model that is the dimensional reduction of supersymmetric Yang-Mills theory in ten dimensions and which has been recently argued to represent the short-distance structure of M theory in the infinite momentum frame. We describe a reduced version of the matrix quantum mechanics and derive the Nicolai map of the simplified supersymmetric matrix model. We use this to argue that there are no phase transitions in the large-N limit, and hence that S-duality is preserved in the full eleven dimensional theory.

hep-th↗

arXiv1996

Gravitational Dressing of Aharonov-Bohm Amplitudes

We investigate Aharonov-Bohm scattering in a theory in which charged bosonic matter fields are coupled to topologically massive electrodynamics and topologically massive gravity. We demonstrate that, at one-loop order, the transmuted spins in this theory are related to the ones of ordinary Chern-Simons gauge theory in the same way that the Knizhnik-Polyakov-Zamolodchikov formula relates the Liouville-dressed conformal weights of primary operators to the bare weights in two-dimensional conformal field theories. We remark on the implications of this connection between two-dimensional conformal field theories and three-dimensional gauge and gravity theories for a topological membrane reformulation of strings. We also discuss some features of the gravitational analog of the Aharonov-Bohm effect.

hep-th↗

arXiv1996

Skyrmions in the quantum Hall effect at finite Zeeman coupling

Using a self consistent approximation for the spin distribution of Skyrmions in the quantum Hall effect, we obtain an effective action for the Skyrmion coordinates. The energy functional is minimised for a periodic distribution of Skyrmions with an underlying hexagonal symetry. We calculate the phonon spectrum of this lattice and find that near the classical minimum, breathing modes of the Skyrmions are strongly suppressed. The resulting equal sized Skyrmions interact via a residual Coulomb potential. Neglecting coupling between phonons and spin waves due to dipole and higher order Coulomb interactions, the Skyrmion crystal has a phonon spectrum identical to that of an electronic Wigner crystal. The transition to a liquid of equal sized Skyrmions is discussed using the theory of dislocation melting and a comparison is made between the predictions of this theory and the results of a recent experiment.

cond-mat↗

arXiv1996

Conformal Dimensions from Topologically Massive Quantum Field Theory

We discuss the evaluation of observables in two-dimensional conformal field theory using the topological membrane description. We show that the spectrum of anomalous dimensions can be obtained perturbatively from the topologically massive quantum field theories by computing radiative corrections to Aharonov-Bohm scattering amplitudes for dynamical charged matter fields. The one-loop corrections in the case of topologically massive Yang-Mills theory are shown to coincide with the scaling dimensions of the induced ordinary and supersymmetric WZNW models. We examine the effects of the dressing of a topologically massive gauge theory by topologically massive gravity and show that the one-loop contributions to the Aharonov-Bohm amplitudes coincide with the leading orders of the KPZ scaling relations for two-dimensional quantum gravity. Some general features of the description of conformal field theories via perturbative techniques in the three-dimensional approach are also discussed.

hep-th↗

arXiv1995

Skyrmion Liquid in SU(2)-invariant Quantum Hall Systems

We report on a theory of the Skyrmion states which occur in quantum Hall regime near certain filling factors. It is shown that in the limit of zero Zeeman splitting in a realistic temperature range the Skyrmion plasma is a liquid described by the effective model of massive two-dimensional Dirac fermions.

cond-mat↗

arXiv1993

Gravitational Dressing of Renormalization Group

We study the gravitational dressing of renormalizable two-dimensional field theories. Our main result is that the one-loop $β$-function is finitely renormalized by the factor ${k+2\over k+1}$, where $k$ is the central charge of the gravitational $SL(2, R)$ current algebra.

hep-th↗

arXiv1992

Induced QCD Without Local Confinement

We examine some properties of the filled Wilson loop observables in the Kazakov-Migdal model of induced QCD. We show that they have a natural interpretation in a modification of the original model in which the $Z_N$ gauge symmetry is broken explicitly by a Wilson kinetic term for the gauge fields. We argue that there are two large N limits of this theory, one leads to ordinary Wilson lattice gauge theory coupled to a dynamical scalar field and the other leads to a version of the Kazakov-Migdal model in which the large N solution found by Migdal can still be used. We discuss the properties of the string theory which emerges.

hep-th↗

arXiv1992

Continuum Limits of ``Induced QCD": Lessons of the Gaussian Model at d=1 and Beyond

We analyze the scalar field sector of the Kazakov--Migdal model of induced QCD. We present a detailed description of the simplest one dimensional {($d$$=$$1$)} model which supports the hypothesis of wide applicability of the mean--field approximation for the scalar fields and the existence of critical behaviour in the model when the scalar action is Gaussian. Despite the ocurrence of various non--trivial types of critical behaviour in the $d=1$ model as $N\rightarrow\infty$, only the conventional large-$N$ limit is relevant for its {\it continuum} limit. We also give a mean--field analysis of the $N=2$ model in {\it any} $d$ and show that a saddle point always exists in the region $m^2>m_{\rm crit}^2(=d)$. In $d=1$ it exhibits critical behaviour as $m^2\rightarrow m_{\rm crit}^2$. However when $d$$>$$1$ there is no critical behaviour unless non--Gaussian terms are added to the scalar field action. We argue that similar behaviour should occur for any finite $N$ thus providing a simple explanation of a recent result of D. Gross. We show that critical behaviour at $d$$>$$1$ and $m^2>m^2_{\rm crit}$ can be obtained by adding a $logarithmic$ term to the scalar potential. This is equivalent to a local modification of the integration measure in the original Kazakov--Migdal model. Experience from previous studies of the Generalized Kontsevich Model implies that, unlike the inclusion of higher powers in the potential, this minor modification should not substantially alter the behaviour of the Gaussian model.

hep-th↗

arXiv1992

Area Law and Continuum Limit in "Induced QCD"

We investigate a class of operators with non-vanishing averages in a D-dimensional matrix model recently proposed by Kazakov and Migdal. Among the operators considered are ``filled Wilson loops" which are the most reasonable counterparts of Wilson loops in the conventional Wilson formulation of lattice QCD. The averages of interest are represented as partition functions of certain 2-dimensional statistical systems with nearest neighbor interactions. The ``string tension" $α'$, which is the exponent in the area law for the ``filled Wilson loop" is equal to the free energy density of the corresponding statistical system. The continuum limit of the Kazakov--Migdal model corresponds to the critical point of this statistical system. We argue that in the large $N$ limit this critical point occurs at zero temperature. In this case we express $α'$ in terms of the distribution density of eigenvalues of the matrix-valued master field. We show that the properties of the continuum limit and the description of how this limit is approached is very unusual and differs drastically from what occurs in both the Wilson theory ($S\propto({\rm Tr}\prod U +{\rm c.c.})$) and in the ``adjoint'' theory ($S\propto\vert{\rm Tr}\prod U\vert^2$). Instead, the continuum limit of the model appears to be intriguingly similar to a $c>1$ string theory.

hep-th↗

arXiv1992

Investigations of Pairing in Anyon Systems

We investigate pairing instabilities in the Fermi-liquid-like state of a single species of anyons. We describe the anyons as Fermions interacting with a Chern-Simons gauge field and consider the weak coupling limit where their statistics approaches that of Fermions. We show that, within the conventional BCS approach, due to induced repulsive Coulomb and current-current interactions, the attractive Aharonov-Bohm interaction is not sufficient to generate a gap in the Fermion spectrum.

cond-mat↗

arXiv1991

Three-Dimensional Gravity and String Ghosts

It is known that much of the structure of string theory can be derived from three-dimensional topological field theory and gravity. We show here that, at least for simple topologies, the string diffeomorphism ghosts can also be explained in terms of three-dimensional physics.

hep-th↗