Physical States in Topological Coset Models

TL;DR

This paper summarizes recent developments in topological coset models, detailing their action, physical state cohomology, and comparisons with minimal models and W_N strings, providing insights into their structure and relations.

Contribution

It presents a detailed analysis of the physical states in topological coset models, including cohomology calculations and comparisons with related models, highlighting new structural understandings.

Findings

Physical states are characterized via BRST-like cohomology.

Cohomology is computed on free field Fock space and Kac-Moody representations.

Results relate topological coset models to minimal models and W_N strings.

Abstract

Recent results about topological coset models are summarized. The action of a topological ${G\over H}$ coset model ($rank\ H = rank\ G$) is written down as a sum of ``decoupled" matter, gauge and ghost sectors. The physical states are in the cohomology of a BRST-like operator that relates these secotrs. The cohomology on a free field Fock space as well as on an irreducible representation of the ``matter" Kac-Moody algebra are extracted. We compare the results with those of $(p,q)$ minimal models coupled to gravity and with $(p,q)$ $W_N$ strings for the case of $A_1^{(1)}$ at level $k={p\over q}-2$ and $A_1^{(N-1)}$ at level $k={p\over q}-N$ respectively.