BRST invariant branching functions of G/H coset models

TL;DR

This paper calculates BRST invariant branching functions for G/H coset models, confirming previous results and deriving new formulas for complex models, ensuring only coset degrees of freedom propagate.

Contribution

It introduces a BRST invariant formula for branching functions in G/H coset models, including new calculations for models not previously analyzed.

Findings

Confirmed previous results for certain models using BRST invariance.

Derived new branching functions for complex coset models.

Validated the approach for models with zero rank(G/H).

Abstract

We compute branching functions of $G/H$ coset models using a BRST invariant branching function formulae, i.e. a branching function that respects a BRST invariance of the model. This ensures that only the coset degrees of freedom will propagate. We consider $G/H$ for rank$(G/H)=0$ models which includes the Kazama-Suzuki construction, and $G_{k_1}\times G_{k_2}/G_{k_1+k_2}$ models. Our calculations here confirm in part previous results for those models which have been obtained under an assumption in a free field approach. We also consider $G_{k_1}\times H_{k_2}/H_{k_1+k_2}$, where $H$ is a subgroup of $G$, and $\prod_{a=1}^mG_{k_a}/G_{\sum_{a=1}^nk_a}$, whose branching functions, to our knowledge, has not been calculated before.