Ghost free dual vector theories in 2+1 dimensions

2005/10/18 by D. Dalmazi · 15 citations
Mathematics · Physics and Astronomy · #Action (physics) #Artificial intelligence #Black Holes and Theoretical Physics #Computer science #Dual (grammatical number) #Dual mode #Duality (order theory) #Embedding #Equivalence (formal languages) #Gauge (firearms) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Philosophy #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Spectrum (functional analysis) #Theoretical physics #hep-th

paper · pdf · doi:10.1088/1126-6708/2006/01/132

published in Journal of High Energy Physics 2006(01), 132 (Springer Nature) · 15 pages, 1 figure

arxiv created 2005/10/18 · openalex publication_date 2006/01/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

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→∞ 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.

Citations

• Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
• Non-commutative Maxwell–Chern–Simons theory in three dimensions and its dual
• Dual embedding of the Lorentz-violating electrodynamics and Batalin-Vilkovisky quantization
• On the dual equivalence of the self-dual and topologically massive B∧F models coupled to dynamical fermionic matter
• On the coupling of the self-dual field to dynamicalU(1) matter and its dual theory
• Equivalence of the Maxwell-Chern-Simons theory and a self-dual model
• Topological and universal aspects of bosonized interacting fermionic systems in 2+1 dimensions
• Perturbative bosonization from two-point correlation functions
• Topologically massive gauge theories

Cited by

• A new spin-2 self-dual model inD= 2+1