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

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

1992-06-21

arxiv.org/abs/hep-th/9206080v1

Nucl.Phys. B395 (1993) 144-166

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/0550-3213(93)90212-8

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.

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