Spacetime Diffeomorphisms and Topological w∞ Symmetry in Two Dimensional Topological String Theory

This paper analyzes spacetime symmetries of topological string theory on a two dimensional torus, and points out that the spacetime geometry of the model is that of the Batalin-Vilkovisky formalism. Previously I found an infinite symmetry algebra in the absolute BRST cohomology of the model. Here I find an analog of the BV ∆ operator, and show that it defines a natural semirelative BRST cohomology. In the absolute cohomology, the ghost-number-zero symmetries form the algebra of all infinitesimal spacetime diffeomorphisms, extended at non-zero ghost numbers to the algebra of all odd-symplectic diffeomorphisms on a spacetime supermanifold. In the semirelative cohomology, the symmetries are reduced to w∞ at ghost number zero, and to a topologically twisted N=2 w∞ superalgebra when all ghost numbers are included. I discuss deformations of the model that break parts of the spacetime symmetries while preserving the topological BRST symmetry on the worldsheet. In the absolute cohomology of the deformed model, another topological w∞ superalgebra may emerge, while the semirelative cohomology leads to a bosonic w∞ symmetry. ⋆ e-mail address: [email protected] † Robert R. McCormick Fellow; research also supported by the NSF under Grant No. PHY90-00386; the DOE under Grant No. DEFG02-90ER40560; the Czech Chart 77 Foundation; and the Czech Acad. Sci. under Grant No. 91-11045.