Chiral gauged Wess-Zumino-Witten theories and coset models in conformal field theory

Abstract

The Wess-Zumino-Witten (WZW) theory has a global symmetry denoted by G L ⊗ G R . In the standard gauged WZW theory, vector gauge fields (i.e. with vector gauge couplings) are in the adjoint representation of the subgroup H ⊂ G. In this paper, we show that, in the conformal limit in two dimensions, there is a gauged WZW theory where the gauge fields are chiral and belong to the subgroups H L and H R where H L and H R can be different groups. In the special case where H L = H R , the theory is equivalent to vector gauged WZW theory. For general groups H L and H R , an examination of the correlation functions (or more precisely, conformal blocks) shows that the chiral gauged WZW theory is equivalent to (G/H) L ⊗(G/H) R coset models in conformal field theory. The equivalence of the vector gauged WZW theory and the corresponding G/H coset theory then follows.

Chiral gauged WZNW models and heterotic string backgrounds

“…It was suggested to 1 We shall mostly consider CWZNW models in the cases when the 'left' and 'right' subgroups are the same. We disagree with the claim [14] that the CWZNW model with H L = H R = H is equivalent to G/H or GWZNW model. cancel the 2d gauge anomaly by introducing an additional world sheet coupling term which corresponds to a non-vanishing target space gauge field background [22].…”

“…It is useful to give the explicit derivation of the expressions for the bosonic and heterotic SL(2, IR)/IR backgrounds using the following parametrisation of the SL(2, IR) group 14 The variables t, x in (7.11) have been rescalled with respect to the original 'classical' variables of the SL(2, IR) group element, i.e. (t, x) → 2/(b + 1) 1/2 (t, x).…”

“…A closely related to GWZNW model is the so called chiral gauged WZNW model [14] (CWZNW) in which one does not include the 'counterterm' Tr (AĀ) in the action [9] (A m = (A,Ā) is a 2d vector field with values in the algebra of H) and thus one has only 'chiral' gauge invariance (with gauge parameters constrained to be holomorphic or antiholomorphic). As we shall see below, the action of CWZNW is, in fact, the only local modification of the GWZNW action which can also be represented in terms of a combination of independent WZNW actions and thus is certainly conformally invariant at the quantum level.…”

Effective theories for 2+1 dimensional non-Abelian topological spin liquids

“…Our strategy is to isolate the gapless sector and construct the underlying conformal field theory. In doing so we keep both chiralities to avoid issues with gauge anomalies [21]. As we shall see, the final picture involves a chiral splitting with each chiral conformal field theory living at the opposite edges of the bulk.…”

“…In other words, the fermionic theory with constraints over the currents (3.43) is equivalent to the gauged-WZW theorỹ 21) in the sense that both of them produce the same correlation functions. Our next task is to show that this gauged-WZW theory follows naturally from a coset Chern-Simons-like bulk theory whenever we define it in the presence of a physical edge.…”