``N=4: A Unifying Framework for 2d Topological Gravity, $c_M\leq 1$ String Theory and Constrained Topological Sigma Model''

TL;DR

This paper reveals a hidden twisted N=4 superconformal symmetry in 2d topological gravity, connects it to $c_M extless=1$ string theory, and explores its relation to a constrained topological sigma model, unifying several frameworks.

Contribution

It uncovers a larger N=4 symmetry in 2d topological gravity and links it to $c_M extless=1$ string theory and a constrained topological sigma model, providing a unifying framework.

Findings

Identification of a twisted N=4 superconformal symmetry in 2d topological gravity.

Establishment of an isomorphism between N=2 structures and $c_M extless=1$ string theory.

Discovery of a mirror algebra corresponding to a 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 $c_M\leq 1$ string theory discussed by Bershadsky et.al. As a byproduct, we find a twisted N=4 structure in $c_M\leq 1$ 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.