On the twisted G/H topological models

TL;DR

This paper explores the construction and analysis of twisted G/H topological models, focusing on specific group choices, introducing non-abelian bosonization, and examining the physical state space via BRST cohomology.

Contribution

It introduces a non-abelian bosonization approach for twisted G/H models and analyzes the physical state space through cohomology, extending understanding of these topological theories.

Findings

Derived the quantum action as a sum of matter, gauge, and ghost sectors.

Computed the cohomology of the BRST charge to identify physical states.

Discussed relations between different G/H models for various subgroup choices.

Abstract

The twisted G/H models are constructed as twisted supersymmetric gauged WZW models. We analyze the case of $G=SU(N)$, $H=SU(N_1)\times ...\times SU(N_n)\times U(1)^r$ with $rank\ G =\ rank\ H$, and discuss possible generalizations. We introduce a non-abelian bosonization of the $(1,0)$ ghost system in the adjoint of $H$ and in G/H. By computing chiral anomalies in the latter picture we write the quantum action as a decoupled sum of ``matter", gauge and ghost sectors. The action is also derived in the unbosonized version. We invoke a free field parametrization and extract the space of physical states by computing the cohomology of $Q$ , the sum of the BRST gauge-fixing charge and the twisted supersymmetry charge. For a given $G$ we briefly discuss the relation between the various G/H models corresponding to different choices of $H$. The choice $H=G$ corresponds to the topological G/G theory.