Induced Dilaton in Topologically Massive Quantum Field Theory

We consider the conformally-invariant coupling of topologically massive gravity to a dynamical massless scalar field theory on a three-manifold with boundary. We show that, in the phase of spontaneously broken Lorentz and Weyl symmetries, this theory induces the target space zero mode of the vertex operator for the string dilaton field on the boundary of the three-dimensional manifold. By a further coupling to topologically massive gauge fields in the bulk, we demonstrate directly from the three-dimensional theory that this dilaton field transforms in the expected way under duality transformations so as to preserve the mass gaps in the spectra of the gauge and gravitational sectors of the quantum field theory. We show that this implies an intimate dynamical relationship between T-duality and S-duality transformations of the quantum string theory. The dilaton in this model couples bulk and worldsheet degrees of freedom to each other and generates a dynamical string coupling.Comment: 26 pages RevTeX, 1 figure, uses epsf.st

Novel Edge States in Self-Dual Gravity

In contrast to the Einstein-Hilbert action, the action for self-dual gravity contains vierbeins. They are eleminated at the level of observables by an $SL(2,\mathbb{C})$ gauge condition implied by the action. We argue that despite this condition, new "edge" or superselected state vectors corresponding to maps of the spheres $S^2_{\infty}$ at infinity to $SL(2, \mathbb{C})$ arise. They are characterised by new quantum numbers and they lead to mixed states. For black holes, they arise both at the horizon and the spatial infinity and may be relevant for the black hole information paradox. Similar comments can be made about the Einstein-Palatini action which uses vierbeins.Comment: 15 pages, reference added, some minor notational changes - no changes in conclusio

Anomalous Defects and Their Quantized Transverse Conductivities

Using a description of defects in solids in terms of three-dimensional gravity, we study the propagation of electrons in the background of disclinations and screw dislocations. We study the situations where there are bound states that are effectively localized on the defect and hence can be described in terms of an effective 1+1 dimensional field theory for the low energy excitations. In the case of screw dislocations, we find that these excitations are chiral and can be described by an effective field theory of chiral fermions. Fermions of both chirality occur even for a given direction of the magnetic field. The ``net'' chirality of the system however is not always the same for a given direction of the magnetic field, but changes from one sign of the chirality through zero to the other sign as the Fermi momentum or the magnitude of the magnetic flux is varied. On coupling to an external electromagnetic field, the latter becomes anomalous, and predicts novel conduction properties for these materials.Comment: New material added. ReVTeX , 31 pgs., 4 figs.(uses epsf

Edge States and Entanglement Entropy

It is known that gauge fields defined on manifolds with spatial boundaries support states localized at the boundaries. In this paper, we demonstrate how coarse-graining over these states can lead to an entanglement entropy. In particular, we show that the entanglement entropy of the ground state for the quantum Hall effect on a disk exhibits an approximate ``area " law.Comment: 16 pages, minor corrections and futher details adde

Catalysis of chiral symmetry breaking by external magnetic fields in three-dimensional lattice QED

The enhancement of the fermionic condensate due to the presence of both homogeneous and non-homogeneous external magnetic fields is studied for three-dimensional QED.Comment: 5 pages, contribution to "Strong and electroweak matter 98", Copenhagen, December 199