Duality and enhanced gauge symmetry in 2 + 1 dimensions

Abstract

We investigate the enlarged CP(N) model in 2+1 dimensions. This is a hybrid of two CP(N) models coupled with each other in a dual symmetric fashion, and it exhibits the gauge symmetry enhancement and radiative induction of the finite off-diagonal gauge boson mass as in the 1+1 dimensional case. We solve the mass gap equations and study the fixed point structure in the large-N limit. We find an interacting ultraviolet fixed point which is in contrast with the 1+1 dimensional case. We also compute the large-N effective gauge action explicitly.

BRST Symmetry and de Rham Cohomology

“…In particular, in Refs. [213,214] an issue of dynamical generation of gauge boson was analyzed in the context of enlarged CP(N) model in lower dimensions. In this model, two complex projective spaces with different coupling constants couple with each other through interactions which preserve exchange of the two spaces.…”

“…It was shown in Refs. [213,214] that the additional gauge field, c , also becomes dynamical through radiative corrections. Moreover, in the self-dual limit where the two running coupling constants become equal, it becomes massless and combines with the two U(1) gauge fields, to yield U(2) Yang-Mills theory.…”

“…In the enlarged model of Refs. [213,214], original gauge fields are auxiliary fields which become dynamical through quantum corrections. From the Hamiltonian point of view, these auxiliary fields could be completely eliminated through equations of motion from the beginning, and the Gauss law constraints could be only implicitly realized.…”

“…When this happens, the Dirac matrix becomes degenerate and the inverse does not exist. From physical point of view, this singular behavior could be associated with a second order phase transition which one encounters in going to the limit r D 1 [213,214].…”

Canonical Analysis of Symmetry Enhancement with Gauged Grassmannian Model

“…One of the most important applications is to the area of generating the masses of the gauge bosons [1]. Recently, the dynamical generation of gauge boson mass has been analyzed in the context of an enlarged CP (N ) model [2]. The model contains a free parameter r which could be understood as an explicit gauge symmetry breaking ⇋ enhancement parameter; in the case of r = 1 the gauge symmetry of the model is U (2), while it is U (1) × U (1) in the case of r = 1.…”