Gauge symmetry enhancement and radiatively induced mass in the largeNnonlinear sigma model

Abstract

We consider a hybrid of nonlinear sigma models in which two complex projective spaces are coupled with each other under a duality. We study the large N effective action in 1ϩ1 dimensions. We find that some of the dynamically generated gauge bosons acquire radiatively induced masses which, however, vanish along the self-dual points where the two couplings characterizing each complex projective space coincide. These points correspond to the target space of the Grassmann manifold along which the gauge symmetry is enhanced, and the theory favors the non-Abelian ultraviolet fixed point.

Duality and enhanced gauge symmetry in 2 + 1 dimensions

“…In order to carry out the path integration in the large N limit, we rewrite the Lagrangian (2.1) in terms of a 2 × 2 hermitian matrix such that 10) where · · · denotes a trace of an N × N matrix. The 2 × 2 matrix operator M is given by…”

“…Therefore, it is important to attempt to extend the previous 1+1 dimensions results of Ref. [10] in order to check whether this is also viable in various other dimensions. In this paper, we take a first step, and extend the previous analysis to 2+1 dimensions.…”

“…[10] that together with the two auxiliary U(1) gauge fields this complex field becomes dynamical through radiative corrections. Moreover, in the self-dual limit where the two running coupling constants become equal, they become massless and combine with the two U(1) fields to yield the U(2) Yang-Mills theory.…”

“…It is well-known that the CP (N) ≡ SU(N)/SU(N − 1) × U (1) model [11] is the prototype of nonlinear sigma model with dynamical generation in which the auxiliary U(1) gauge field becomes dynamical through the radiative corrections in the large-N limit [6]. In the recently proposed extension [10] of the CP (N) model, two complex projective spaces with different coupling constants have mutual interactions which are devised in such a way to preserve the duality between the two spaces. In addition to the two auxiliary U(1) gauge fields which stand for each complex projective space, one extra auxiliary complex gauge field is introduced to derive the interactions with duality.…”

“…Recently, some new properties have been explored in relation with the dynamical generation of gauge bosons, that is, the gauge symmetry enhancement and radiatively induced finite gauge boson mass in 1+1 dimensions [10]. It is well-known that the CP (N) ≡ SU(N)/SU(N − 1) × U (1) model [11] is the prototype of nonlinear sigma model with dynamical generation in which the auxiliary U(1) gauge field becomes dynamical through the radiative corrections in the large-N limit [6].…”