$c_M<1$ String Theory as a Constrained Topological Sigma Model

Details $c_M<1$ String Theory as a Constrained Topological Sigma Model $c_M<1$ String Theory as a Constrained Topological Sigma Model

1994-10-31

arxiv.org/abs/hep-th/9410233v1

Phys.Lett.B345:6-14,1995

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, Latex file, UG-9/94

Scientific paper

10.1016/0370-2693(94)01618-M

It has been argued by Ishikawa and Kato that by making use of a specific bosonization, $c_M=1$ string theory can be regarded as a constrained topological sigma model. We generalize their construction for any $(p,q)$ minimal model coupled to two dimensional (2d) gravity and show that the energy--momentum tensor and the topological charge of a constrained topological sigma model can be mapped to the energy--momentum tensor and the BRST charge of $c_M<1$ string theory at zero cosmological constant. We systematically study the physical state spectrum of this topological sigma model and recover the spectrum in the absolute cohomology of $c_M<1$ string theory. This procedure provides us a manifestly topological representation of the continuum Liouville formulation of $c_M<1$ string theory.

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