Two Dimensional String Theory and the Topological Torus

Abstract

We analyze topological string theory on a two dimensional torus, focusing on symmetries in the matter sector. Even before coupling to gravity, the topological torus has an infinite number of point-like physical observables, which give rise via the BRST descent equations to an infinite symmetry algebra of the model. The point-like observables of ghost number zero form a topological ground ring, whose generators span a spacetime manifold; the symmetry algebra represents all (ground ring valued) diffeomorphisms of the spacetime. At nonzero ghost numbers, the topological ground ring is extended to a superring, the spacetime manifold becomes a supermanifold, and the symmetry algebra preserves a symplectic form on it. In a decompactified limit of cylindrical target topology, we find a nilpotent charge which behaves like a spacetime topological BRST operator. After coupling to topological gravity, this model might represent a topological phase of $c=1$ string theory. We also point out some analogies to two dimensional superstrings with the chiral GSO projection, and to string theory with $c=-2$.

22 pages, no figures

References in corpus (11)

• Algebraic Structures and Differential Geometry in 2D String Theory
• Interaction of Discrete States in Two-Dimensional String Theory
• Ground Rings and Their Modules in 2D Gravity with $c\le 1$ Matter
• Gauge Theory Formulation of the $c=1$ Matrix Model: Symmetries and Discrete States
• Some Properties of (Non) Critical Strings
• Ward Identities in Two-Dimensional String Theory
• Bosonization of Nonrelativistic Fermions and W-infinity Algebra
• Ground ring for the 2D NSR string
• $W$-Infinity Ward Identities and Correlation Functions in the $C=1$ Matrix Model
• Operator Product Expansion and Topological States in $c=1$ Matter Coupled to 2-D Gravity
• Puncture Operator in c=1 Liouville Gravity

Cited by in corpus (11)

• Consistent couplings between fields with a gauge freedom and deformations of the master equation
• Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories
• On operad structures of moduli spaces and string theory
• Large N 2D Yang-Mills Theory and Topological String Theory
• Two dimensional black-hole as a topological coset model of c=1 string theory
• Topological Rigid String Theory and Two Dimensional QCD
• Topological Landau-Ginzburg Model of Two-Dimensional String Theory
• Equivariant Topological Sigma Models
• Liouville D-branes in Two-Dimensional Strings and Open String Field Theory
• Spacetime Diffeomorphisms and Topological W-Infinity Symmetry in Two Dimensional Topological String Theory
• $c_M<1$ String Theory as a Constrained Topological Sigma Model