A Coherent State Path Integral for Anyons

We derive an $su(1,1)$ coherent state path integral formula for a system of two one-dimensional anyons in a harmonic potential. By a change of variables we transform this integral into a coherent states path integral for a harmonic oscillator with a shifted energy. The shift is the same as the one obtained for anyons by other methods. We justify the procedure by showing that the change of variables corresponds to a $su(1,1)$ version of the Holstein-Primakoff transformation.Comment: Latex 6 pages, USITP-94-1

The QCD Trace Anomaly as a Vacuum Effect (The vacuum is a medium is the message!)

We use arguments taken from the electrodynamics of media to deduce the QCD trace anomaly from the expression for the vacuum energy in the presence of an external color magnetic field.Comment: 18 pages, USITP 94-1

Discretization of the Superparticle Path Integral

Requiring that the path integral has the global symmetries of the classical action and obeys the natural composition property of path integrals, and also that the discretized action has the correct naive continuum limit, we find a viable discretization of the (D=3,N=2) superparticle action.Comment: 10 page

The Quantum Geometry of N=(2,2) Non-Linear Sigma-Models

We consider a general N=(2,2) non-linear sigma-model in (2,2) superspace. Depending on the details of the complex structures involved, an off-shell description can be given in terms of chiral, twisted chiral and semi-chiral superfields. Using superspace techniques, we derive the conditions the potential has to satisfy in order to be ultra-violet finite at one loop. We pay particular attention to the effects due to the presence of semi-chiral superfields. A complete description of N=(2,2) strings follows from this.Comment: 9 pages, Late

The influence of the Hall force on the vortex dynamics in type II superconductors

The effect of the Hall force on the pinning of vortices in type II superconductors is considered. A field theoretic formulation of the pinning problem allows a non-perturbative treatment of the influence of quenched disorder. A self-consistent theory is constructed using the diagrammatic functional method for the effective action, and an expression for the pinning force for independent vortices as well as vortex lattices is obtained. We find that the pinning force for a single vortex is suppressed by the Hall force at low temperatures while it is increased at high temperatures. The effect of the Hall force is more pronounced on a single vortex than on a vortex lattice. The results of the self-consistent theory are shown to be in good agreement with numerical simulations.Comment: 9 pages, 4 figures, published in Physical Review

Global Anomalies and Anyons in 1+1 Dimensions

We consider the analog in one spatial dimension of the Bose-Fermi transmutation for planar systems. A quantum mechanical system of a spin 1/2 particle coupled to an abelian gauge field, which is classically invariant under gauge transformations and charge conjugation is studied. It is found that unless the flux enclosed by the particle orbits is quantized, and the spin takes a value $n+ 1/2$, at least one of the two symmetries would be anomalous. Thus, charge conjugation invariance and the existence of abelian instantons simultaneously force the particles to be either bosons or fermions, but not anyons.Comment: Changed title. To be published in Physics Letters

The Polyakov action on the supertorus

A consistent method for obtaining a well-defined Polyakov action on the supertorus is presented. This method uses the covariantization of derivative operators and enables us to construct a Polyakov action which is globally defined.Comment: 15 pages LaTe

The N=4 string is the same as the N=2 string

We redo the quantization of the N=4 string, taking into account the reducibility of the constraints. The result is equivalent to the N=2 string, with critical dimension D=4 and signature (++--). The N=4 formulation has several advantages: the sigma-model field equations are implied classically, rather than by quantum/beta-function calculations; self-duality/chirality is one of the super-Virasoro constraints; SO(2,2) covariance is manifest. This reveals that the theory includes fermions, and is apparently spacetime supersymmetric.Comment: 7 pg (uuencoded dvi file; otherwise same as original

Hyperkahler sigma models on cotangent bundles of Hermitian symmetric spaces using projective superspace

Kahler manifolds have a natural hyperkahler structure associated with (part of) their cotangent bundles. Using projective superspace, we construct four-dimensional N = 2 models on the tangent bundles of some classical Hermitian symmetric spaces (specifically, the four regular series of irreducible compact symmetric Kahler manifolds, and their non-compact versions). A further dualization yields the Kahler potential for the hyperkahler metric on the cotangent bundle.Comment: 47 pages, typos corrected, version accepted by JHE