H. Kanno — Page 2 | Searcharxiv

arXiv1992

BRST cohomology ring in 2D gravity coupled to minimal models

The ring structure of Lian-Zuckerman states for $(q,p)$ minimal models coupled to gravity is shown to be ${\cal R}={\cal R}_0\otimes {\bf C} [w,w^{-1}]$ where ${\cal R}_0$ is the ring of ghost number zero operators generated by two elements and $w$ is an operator of ghost number $-1$. Some examples are discussed in detail. For these models the currents are also discussed and their algebra is shown to contain the Virasoro algebra.

hep-th↗

arXiv1992

SO(2,C) invariant ring structure of BRST cohomology and singular vectors in 2D gravity with c < 1 matter

We consider BRST quantized 2D gravity coupled to conformal matter with arbitrary central charge $c^M = c(p,q) < 1$ in the conformal gauge. We apply a Lian-Zuckerman $SO(2,\bbc)$ ($(p,q)$ - dependent) rotation to Witten's $c^M = 1$ chiral ground ring. We show that the ring structure generated by the (relative BRST cohomology) discrete states in the (matter $\otimes$ Liouville $\otimes$ ghosts) Fock module may be obtained by this rotation. We give also explicit formulae for the discrete states. For some of them we use new formulae for $c <1$ Fock modules singular vectors which we present in terms of Schur polynomials generalizing the $c=1$ expressions of Goldstone, while the rest of the discrete states we obtain by finding the proper $SO(2,\bbc)$ rotation. Our formulae give the extra physical states (arising from the relative BRST cohomology) on the boundaries of the $p \times q$ rectangles of the conformal lattice and thus all such states in $(1,q)$ or $(p,1)$ models.

hep-th↗