Ghost free dual vector theories in 2+1 dimensions

Abstract

We explore here the issue of duality versus spectrum equivalence in abelian vector theories in 2+1 dimensions. Specifically we examine a generalized self-dual (GSD) model where a Maxwell term is added to the self-dual model. A gauge embedding procedure applied to the GSD model leads to a Maxwell-Chern-Simons (MCS) theory with higher derivatives. We show that the latter contains a ghost mode contrary to the original GSD model. On the other hand, the same embedding procedure can be applied to $N_f$ fermions minimally coupled to the self-dual model. The dual theory corresponds to $N_f$ fermions with an extra Thirring term coupled to the gauge field via a Pauli-like term. By integrating over the fermions at $N_f\to \infty$ in both matter coupled theories we obtain effective quadratic theories for the corresponding vector fields. On one hand, we have a nonlocal type of the GSD model. On the other hand, we have a nonlocal form of the MCS theory. It turns out that both theories have the same spectrum and are ghost free. By figuring out why we do not have ghosts in this case we are able to suggest a new master action which takes us from the local GSD to a nonlocal MCS model with the same spectrum of the original GSD model and ghost free. Furthermore, there is a dual map between both theories at classical level which survives quantum correlation functions up to contact terms. The remarks made here may be relevant for other applications of the master action approach.

arXiv comment15 pages, 1 figure

References in corpus (25)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• The Fermion-Boson Mapping in Three Dimensional Quantum Field Theory
• Dual equivalence between Self-Dual and Maxwell-Chern-Simons models coupled to dynamical U(1) charged matter
• On the equivalence of the self-dual and Maxwell-Chern-Simons models coupled to Fermions
• On the Equivalence of the Maxwell-Chern-Simons Theory and a Self-Dual Model
• Duality Equivalence Between Self-Dual And Topologically Massive Non-Abelian Models
• Dual embedding of the Lorentz-violating electrodinamics and Batalin-Vilkovisky quantization
• Gauge Invariance and Duality in the Noncommutative Plane
• Topological and Universal Aspects of Bosonized Interacting Fermionic Systems in (2+1)d
• Bosonization and Duality of Massive Thirring Model
• Duality in Noncommutative Topologically Massive Gauge Field Theory Revisited
• Issues of duality on non-commutative manifolds: the {\it non-equivalence} between self-dual and topologically massive models
• Noncommutative Maxwell-Chern-Simons theory in three dimensions and its dual
• On the dual equivalence of the Born-Infeld-Chern-Simons model coupled to dynamical U(1) charged matter
• Dual equivalence in models with higher-order derivatives
• Parent Action Approach for the Duality between Non-Abelian Self-Dual and Yang-Mills-Chern-Simons Models
• On the dual equivalence of the self-dual and topologically massive $B\wedge F$ models coupled to dynamical fermionic matter
• On the relation between the propagators of dual theories
• On the coupling of the self-dual field to dynamical U(1) Matter and its dual theory
• Bosonization and Duality in Arbitrary Dimensions: New Results
• The static potential in QED${}_3$ with non-minimal coupling
• Some Quantum Aspects of Complex Vector Fields with Chern-Simons Term
• A New Approach for Bosonization of Massive Thirring Model in Three Dimensions
• Perturbative bosonization from two-point correlation functions
• Conflict between symmetries: a classical example

Cited by in corpus (10)

• Leptogenesis in the Universe
• A new spin-2 self-dual model in $D=2+1$
• Dual descriptions of spin two massive particles in $D=2+1$ via master actions
• Generalized duality between local vector theories in $D=2+1$
• Duality of parity doublets of helicity $\pm 2$ in $D=2+1$
• Dual descriptions of massive spin-3 particles in $D=2+1$ via Noether gauge embedment
• Dual embedding of extended models with a Lorentz-breaking mass term
• Quantum equivalence between the self-dual and the Maxwell-Chern-Simons models nonlinearly coupled to U(1) scalar fields
• The self-dual Lorentz violating model: quantization, scattering and dual equivalence
• Tree-level equivalence between a Lorentz-violating extension of QED and its dual model in electron-electron scattering