A Unifying Framework for 2 d Topological Gravity , c M ≤ 1 String Theory and Constrained Topological Sigma Model

Abstract

It is shown that two dimensional (2d) topological gravity in the conformal gauge has a larger symmetry than has been hitherto recognized; in the formulation of Labastida, Pernici and Witten it contains a twisted " small " N = 4 superconformal symmetry. There are in fact two distinct twisted N = 2 structures within this N = 4, one of which is shown to be isomorphic to the algebra discussed by the Verlindes and the other corresponds, through bosonization, to c M ≤ 1 string theory discussed by Bershadsky et.al. As a byproduct, we find a twisted N = 4 structure in c M ≤ 1 string theory. We also study the " mirror " of this twisted N = 4 algebra and find that it corresponds, through another bosonization, to a constrained topological sigma model in complex dimension one.

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