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 Nonlinear Multiplet Revisited

Using a reformulation of the nonlinear multiplet as a gauge multiplet, we discuss its dynamics. We show that the nonlinear ``duality'' that appears to relate the model to a conventional $\sigma$-model introduces a new sector into the theory.Comment: 11 pages, ITP-SB-94-23, USITP-94-1

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

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

New N=4 Superfields and Sigma-models

In this note, we construct new representations of D=2, N=4 supersymmetry which do not involve chiral or twisted chiral multiplets. These multiplets may make it possible to circumvent no-go theorems about N=4 superspace formulations of WZWN-models.Comment: 11 pages, late

Spin Factor in Path Integral Representation for Dirac Propagator in External Fields

We study the spin factor problem both in $3+1$ and $2+1$ dimensions which are essentially different for spin factor construction. Doing all Grassmann integrations in the corresponding path integral representations for Dirac propagator we get representations with spin factor in arbitrary external field. Thus, the propagator appears to be presented by means of bosonic path integral only. In $3+1$ dimensions we present a simple derivation of spin factor avoiding some unnecessary steps in the original brief letter (Gitman, Shvartsman, Phys. Lett. {\bf B318} (1993) 122) which themselves need some additional justification. In this way the meaning of the surprising possibility of complete integration over Grassmann variables gets clear. In $2+1$ dimensions the derivation of the spin factor is completely original. Then we use the representations with spin factor for calculations of the propagator in some configurations of external fields. Namely, in constant uniform electromagnetic field and in its combination with a plane wave field.Comment: 34 pages, LaTe

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

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

On the scattering amplitude in the Aharonov-Bohm gauge field

A general expression for the scattering amplitude of nonrelativistic spinless particles in the Aharonov-Bohm gauge potential is obtained within the time independent formalism. The result is valid also in the backward and forward directions as well as for any choice of the boundary conditions on the wave function at the flux tube position.Comment: 18 pages, plain TE

New massive supergravity multiplets

We present new off-shell formulations for the massive superspin-3/2 multiplet. In the massless limit, they reduce respectively to the old minimal (n=-1/3) and non-minimal ($n\neq -1/3, 0$) linearized formulations for 4D N=1 supergravity. Duality transformations, which relate the models constructed, are derived.Comment: 18 pages, LaTeX; v2: minor changes, references adde