Making Sense of Singular Gauge Transformations in 1+1 and 2+1 Fermion Models

We study the problem of decoupling fermion fields in 1+1 and 2+1 dimensions, in interaction with a gauge field, by performing local transformations of the fermions in the functional integral. This could always be done if singular (large) gauge transformations were allowed, since any gauge field configuration may be represented as a singular pure gauge field. However, the effect of a singular gauge transformation of the fermions is equivalent to the one of a regular transformation with a non-trivial action on the spinorial indices. For example, in the two dimensional case, singular gauge transformations lead naturally to chiral transformations, and hence to the usual decoupling mechanism based on Fujikawa Jacobians. In 2+1 dimensions, using the same procedure, different transformations emerge, which also give rise to Fujikawa Jacobians. We apply this idea to obtain the v.e.v of the fermionic current in a background field, in terms of the Jacobian for an infinitesimal decoupling transformation, finding the parity violating result.Comment: 14 pages, Late

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

Tunneling between fermionic vacua and the overlap formalism

The probability amplitude for tunneling between the Dirac vacua corresponding to different signs of a parity breaking fermionic mass $M$ in $2+1$ dimensions is studied, making contact with the continuum overlap formulation for chiral determinants. It is shown that the transition probability in the limit when $M \to \infty$ corresponds, via the overlap formalism, to the squared modulus of a chiral determinant in two Euclidean dimensions. The transition probabilities corresponding to two particular examples: fermions on a torus with twisted boundary conditions, and fermions on a disk in the presence of an external constant magnetic field are evaluated.Comment: Reference added. 12 pages, LateX, no figure

Chiral zero modes in non local domain walls

We study a generalization of the Callan-Harvey mechanism to the case of a non local mass. Using a 2+1 model as a concrete example, we show that both the existence and properties of localized zero modes can also be consistently studied when the mass is non local. After dealing with some general properties of the resulting integral equations, we show how non local masses naturally arise when radiative corrections are included. We do that for a 2+1 dimensional example, and also evaluate the zero mode of the resulting non local Dirac operator.Comment: 20 pages, LaTeX, 4 figures; typos and content of sections 2 and 3 correcte

Regularized overlap and the chiral determinant

We study the relationship between the continuum overlap and its corresponding chiral determinant, showing that the former amounts to an unregularised version of the latter. We then construct a regularised continuum overlap, and consider the chiral anomalies that follow therefrom. The relation between these anomalies and the ones derived from the formal (i.e., unregularised) overlap is elucidated.Comment: 14 pages, late

One-loop effects in a self-dual planar noncommutative theory

We study the UV properties, and derive the explicit form of the one-loop effective action, for a noncommutative complex scalar field theory in 2+1 dimensions with a Grosse-Wulkenhaar term, at the self-dual point. We also consider quantum effects around non-trivial minima of the classical action which appear when the potential allows for the spontaneous breaking of the U(1) symmetry. For those solutions, we show that the one-loop correction to the vacuum energy is a function of a special combination of the amplitude of the classical solution and the coupling constant.Comment: Version to appear in JHE

Massless Fermions and the Instanton Dipole Liquid in Compact QED_3

We study the consequences of including parity preserving matter for the effective dual theory corresponding to compact QED_3; in particular we focus on the effect of that contribution on the confinement-deconfinement properties of the system. To that end, we compare two recent proposals when massless fermions are included, both based on an effective anomalous dual model, but having global and local Z_2 symmetries, respectively. We present a detailed analysis to show that while for large mass fermions the global Z_2 symmetry is preferred, in the massless fermion case the local Z_2 scenario turns out to be the proper one. We present a detailed discussion about how the inclusion of massless fermions in compact QED_3 leads to deconfinement, and discuss the stability of the deconfined phase by introducing a description based on an instanton dipole liquid picture.Comment: 28 page

On Coordinate Transformations in Planar Noncommutative Theories

We consider planar noncommutative theories such that the coordinates verify a space-dependent commutation relation. We show that, in some special cases, new coordinates may be introduced that have a constant commutator, and as a consequence the construction of Field Theory models may be carried out by an application of the standard Moyal approach in terms of the new coordinates. We apply these ideas to the concrete example of a noncommutative plane with a curved interface. We also show how to extend this method to more general situations.Comment: 20 pages, 1 figure. references adde

On the chiral and deconfinement phase transitions in parity-conserving QED_3 at finite temperature

We present some results about the interplay between the chiral and deconfinement phase transitions in parity-conserving QED3 (with N flavours of massless 4 component fermions) at finite temperature. Following Grignani et al (Phys. Rev. D53, 7157 (1996), Nucl. Phys. B473, 143 (1996)), confinement is discussed in terms of an effective Sine-Gordon theory for the timelike component of the gauge field A_0. But whereas in the references above the fermion mass m is a Lagrangian parameter, we consider the m=0 case and ask whether an effective S-G theory can again be derived with m replaced by the dynamically generated mass Sigma which appears below T_{ch}, the critical temperature for the chiral phase transition. The fermion and gauge sectors are strongly interdependent, but as a first approximation we decouple them by taking Sigma to be a constant, depending only on the constant part of the gauge field. We argue that the existence of a low-temperature confining phase may be associated with the generation of Sigma; and that, analogously, the vanishing of Sigma for T > T_{ch} drives the system to its deconfining phase. The effect of the gauge field dynamics on mass generation is also indicated. (38kb)Comment: 1 reference adde

Integrability and Conformal Symmetry in the BCS model

The exactly solvable BCS Hamiltonian of superconductivity is considered from several viewpoints: Richardson's ansatz, conformal field theory, integrable inhomogenous vertex models and Chern-Simons theory.Comment: Latex with macros included, 12 pages, Proceedings of the NATO Advanced Research Workshop on Statistical Field Theories, Como 18-23 June 2001. Editors: Andrea Cappelli and Giuseppe Mussardo. to be published by Kluwer, Academic Publishers. Corrected some typos and further acknowledgment