Non-Critical String Models as Topological Coset models

Abstract

The topological coset model appraoch to non-critical string models is summarized. The action of a topological twisted $\frac{G}{H}$ coset model ($rankH=rankG$) is written down. A ``topological coset algebra" is derived and compared with the algebraic structure of the $N=2$ twisted models. The cohomology on a free field Fock space as well as on the space of irreducible representation of the ``matter" \ala are extracted. We compare the results of the $A_1^{(N-1)}$ at level $k=\frac{p}{q}-N$ with those of $(p,q)$ $W_N$ strings. A $\frac{SL(2,R)}{SL(2,R)}$ model which corresponds to the $c=1$ is written down. A similarity transformation on the BRST charge enables us to extract the full BRST cohomoloy. One to one correspondence between the physical states of the $c=1$ and the corresponding coset model is found. Talk presented at ``Strings' 93", May 93 Berekely.}

18 pages