Chiral Rings and Physical States in c<1 String Theory

Abstract

We show how the double cohomology of the String and Felder BRST charges naturally leads to the ring structure of $c<1$ strings. The chiral ring is a ring of polynomials in two variables modulo an equivalence relation of the form $x^p\simeq y^{p+1}$ for the (p+1,p) model. We also study the states corresponding to the edges of the conformal grid whose inclusion is crucial for the closure of the ring. We introduce candidate operators that correspond to the observables of the matrix models. Their existence is motivated by the relation of one of the screening operators of the minimal model to the zero momentum dilaton.

20 pages, harvmac, 4 figures (drawn using LaTeX appended to the end of the file), IMSc--92/30

References in corpus (5)

• Algebraic Structures and Differential Geometry in 2D String Theory
• BRST Analysis of Physical States for 2D (Super) Gravity Coupled to (Super) Conformal Matter
• Ground Rings and Their Modules in 2D Gravity with $c\le 1$ Matter
• SO(2,C) invariant ring structure of BRST cohomology and singular vectors in 2D gravity with c < 1 matter
• States of non-zero ghost number in $c<1$ matter coupled to 2d gravity

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• Minimal Superstrings and Loop Gas Models
• Matrix Model and Time-like Linear Dilaton Matter
• Genus Zero Correlation Functions in c<1 String Theory
• Correlation Functions and Multicritical Flows in $c<1$ String Theory
• Observations on the Topological Structure in 2d Gravity Coupled to Minimal Matter
• $c_M<1$ String Theory as a Constrained Topological Sigma Model
• Ring of physical states in the M(2,3) Minimal Liouville gravity