Dynamical Domain Wall Defects in 2+1 Dimensions

We study some dynamical properties of a Dirac field in 2+1 dimensions with spacetime dependent domain wall defects. We show that the Callan and Harvey mechanism applies even to the case of defects of arbitrary shape, and in a general state of motion. The resulting chiral zero modes are localized on the worldsheet of the defect, an embedded curved two dimensional manifold. The dynamics of these zero modes is governed by the corresponding induced metric and spin connection. Using known results about determinants and anomalies for fermions on surfaces embedded in higher dimensional spacetimes, we show that the chiral anomaly for this two dimensional theory is responsible for the generation of a current along the defect. We derive the general expression for such a current in terms of the geometry of the defect, and show that it may be interpreted as due to an "inertial" electric field, which can be expressed entirely in terms of the spacetime curvature of the defects. We discuss the application of this framework to fermionic systems with defects in condensed matter.Comment: 12 pages, Late

A doubled discretisation of abelian Chern-Simons theory

A new discretisation of a doubled, i.e. BF, version of the pure abelian Chern-Simons theory is presented. It reproduces the continuum expressions for the topological quantities of interest in the theory, namely the partition function and correlation function of Wilson loops. Similarities with free spinor field theory are discussed which are of interest in connection with lattice fermion doubling.Comment: 5 pages, revtex, 2 ps figures (epsf required). To appear in Phys.Rev.Let

Fermionic String from Abelian Higgs Model with monopoles and Θ\Theta-term

The four dimensional Abelian Higgs model with monopoles and $\Theta$-term is considered in the limit of the large mass of the higgs boson. We show that for $\Theta=2 \pi$ the theory is equivalent, at large distances, to summation over all possible world-sheets of fermionic strings with Dirichlet type boundary conditions on string coordinates.Comment: 8 pages, LaTeX file, no figures. Submitted to JETP Let

The 3d Ising Model represented as Random Surfaces

We consider a random surface representation of the three-dimensional Ising model.The model exhibit scaling behaviour and a new critical index \k which relates \g_{string} for the bosonic string to the exponent \a of the specific heat of the 3d Ising model is introduced. We try to determine \k by numerical simulations.Comment: No figures included. Available by ordinary mail on request. 13 pages. Latex. preprint NBI-HE-92-8

Edge Excitations of an Incompressible Fermionic Liquid in a Disorder Magnetic Field

The model of lattice fermions in 2+1 dimensional space is formulated, the critical states of which are lying in the basis of such physical problems, as 3D Ising Model(3DIM) and the edge excitations in the Hall effect. The action for this exitations coincides with the action of so called sign-factor model in 3DIM at one values of its parameters, and represent a model for the edge excitations, which are responsible for the plato transitions in the Hall effect, at other values. The model can be formulated also as a loop gas models in 2D, but unlikely the O(n) models, where the loop fugacity is real, here we have directed (clochwise and conterclochwise) loops and phase factors $e^{\pm 2\pi {p \over q} i}$ for them. The line of phase transitions in the parametric space will be found and corresponding continuum limits of this models will be constructed. It appears, that besides the ordinary critical line, which separates the dense and diluted phases of the models(like in ordinary O(n) models), there is a line, which corresponds to the full covering of the space by curves. The N=2 twisted superconformal models with SU(2)/U(1) coset model coupling constant $k={q \over p}-2$ describes this states.Comment: 29 pages, latex, 3 latex figures include

New Superembeddings for Type II Superstrings

Possible ways of generalization of the superembedding approach for the supersurfaces with the number of Grassmann directions being less than the half of that for the target superspace are considered on example of Type II superstrings. Focus is on n=(1,1) superworldsheet embedded into D=10 Type II superspace that is of the interest for establishing a relation with the NSR string.Comment: 26 pages, LaTeX, JHEP.cls and JHEP.bst style files are used; v2: misprints corrected, comments, acknowledgments, references adde

Lorentz harmonics and superfield action. D=10, N=1 superstring

We propose a new version of the superfield action for a closed D=10, N=1 superstring where the Lorentz harmonics are used as auxiliary superfields. The incorporation of Lorentz harmonics into the superfield action makes possible to obtain superfield constraints of the induced worldsheet supergravity as equations of motion. Moreover, it becomes evident that a so-called 'Wess-Zumino part' of the superfield action is basically a Lagrangian form of the generalized action principle. We propose to use the second Noether theorem to handle the essential terms in the transformation lows of hidden gauge symmetries, which remove dynamical degrees of freedom from the Lagrange multiplier superfield.Comment: 23 pages, latex, no figures. V.2, minor corrections, a reference adde

Superstring action in AdS_5 x S^5: kappa symmetry light cone gauge

As part of program to quantize superstrings in AdS_5 x S^5 background in light cone approach we find the explicit form of the corresponding Green-Schwarz action in fermionic light-cone kappa-symmetry gauge. The resulting action is quadratic and quartic in fermions. In the flat space limit it reduces to the standard light-cone Green-Schwarz action, and also has the correct superparticle limit. We discuss fixing the bosonic light-cone gauge and a reformulation of the action in terms of 2-d Dirac spinors.Comment: 32 pages, latex. v4: misprints corrected in Appendix A, to appear in Phys Rev

SUPERSTRINGS AND SUPERMEMBRANES IN THE DOUBLY SUPERSYMMETRIC GEOMETRICAL APPROACH

We perform a generalization of the geometrical approach to describing extended objects for studying the doubly supersymmetric twistor--like formulation of super--p--branes. Some basic features of embedding world supersurface into target superspace specified by a geometrodynamical condition are considered. It is shown that the main attributes of the geometrical approach, such as the second fundamental form and extrinsic torsion of the embedded surface, and the Codazzi, Gauss and Ricci equations, have their doubly supersymmetric counterparts. At the same time the embedding of supersurface into target superspace has its particular features. For instance, the embedding may cause more rigid restrictions on the geometrical properties of the supersurface. This is demonstrated with the examples of an N=1 twistor--like supermembrane in D=11 and type II superstrings in D=10, where the geometrodynamical condition causes the embedded supersurface to be minimal and puts the theories on the mass shell.Comment: 45 pages, LaTeX, 3 appendicie

Precision calculation of 1/4-BPS Wilson loops in AdS(5) x S-5

We study the strong coupling behaviour of 1/4-BPS circular Wilson loops (a family of “latitudes”) in N=4 Super Yang-Mills theory, computing the one-loop corrections to the relevant classical string solutions in AdS5 ×S5. Supersymmetric localization provides an exact result that, in the large ’t Hooft coupling limit, should be reproduced by the sigma-model approach. To avoid ambiguities due to the absolute normalization of the string partition function, we compare the ratio between the generic latitude and the maximal 1/2-BPS circle: any measure-related ambiguity should simply cancel in this way. We use the Gel’fand-Yaglom method with Dirichlet boundary conditions to calculate the relevant functional determinants, that present some complications with respect to the standard circular case. After a careful numerical evaluation of our final expression we still find disagreement with the localization answer: the difference is encoded into a precise “remainder function”. We comment on the possible origin and resolution of this discordance