Kleinian Singularities and the Ground Ring of C=1 String Theory

Abstract

We investigate the nature of the ground ring of c=1 string theory at the special A-D-E points in the c=1 moduli space associated to discrete subgroups of SU(2). The chiral ground rings at these points are shown to define the A-D-E series of singular varieties introduced by Klein. The non-chiral ground rings relevant to closed-string theory are 3 real dimensional singular varieties obtained as U(1) quotients of the Kleinian varieties. The unbroken symmetries of the theory at these points are the volume-preserving diffeomorphisms of these varieties. The theory of Kleinian singularities has a close relation to that of complex hyperKahler surfaces, or gravitational instantons. We speculate on the relevance of these instantons and of self-dual gravity in c=1 string theory.

26 pages, Phyzzx macro, TIFR/TH/92-34

References in corpus (6)

• Algebraic Structures and Differential Geometry in 2D String Theory
• Interaction of Discrete States in Two-Dimensional 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
• The Master Equation of 2D String Theory
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• Matrix Model and Time-like Linear Dilaton Matter
• Closed string tachyons, flips and conifolds
• ABCD of Beta Ensembles and Topological Strings
• Notes on a singular Landau-Ginzburg family
• Noncritical-Topological Correspondence: Disc Amplitudes and Noncompact Branes