Realization of $W_{1+\infty }$ and Virasoro Algebras in Supersymmetric Theories on Four Manifolds

Abstract

We demonstrate that a supersymmetric theory twisted on a Kähler four manifold $M={\Sigma }_1\times {\Sigma }_2,$ where ${\Sigma }_{1,2}$ are 2D Riemann surfaces, possesses a "left-moving" conformal stress tensor on ${\Sigma }_1$ (${\Sigma }_2$) in the BRST cohomology. The central charge of the Virasoro algebra has a purely geometric origin and is proportional to the Euler characteristic of the ${\Sigma }_2$ (${\Sigma }_1$) surface. This structure is shown to be invariant under renormalization group. We also give a representation of the algebra $W_{1+\infty }$ in terms of a free chiral supermultiplet.

Latex, 13 pages, NBI-HE-94-35. Minor stylistic changes

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