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

Debashis Ghoshal·Dileep P. Jatkar·Sunil Mukhi
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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.

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Debashis Ghoshal, Dileep P. Jatkar, Sunil Mukhi. 1992-06-21. Kleinian Singularities and the Ground Ring of C=1 String Theory. https://doi.org/10.1016/0550-3213(93)90212-8

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