Topological string theory

About: Topological string theory is a research topic. Over the lifetime, 1206 publications have been published within this topic receiving 54758 citations.

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 $c=-2$.

Topological background fields as quantum degrees of freedom of compactified strings

Abstract: It is shown that background fields of a topological character usually introduced as such in compactified string theories correspond to quantum degrees of freedom which parametrise the freedom in choosing a representation of the zero mode quantum algebra in the presence of non-trivial topology. One consequence would appear to be that the values of such quantum degrees of freedom, in other words of the associated topological background fields, cannot be determined by the nonperturbative string dynamics. Comment: 1+10 pages, no figures

Holomorphic Yang-Mills theory and variation of the Donaldson invariants

Abstract: We study the path integrals of the holomorphic Yang-Mills theory on compact K\"{a}hler surface with $b_2^+ = 1$. Based on the results, we examine the correlation functions of the topological Yang-Mills theory and the corresponding Donaldson invariants as well as their transition formulas.

Wrapped membranes, matrix string theory and an infinite dimensional Lie algebra

Abstract: We examine the algebraic structure of the matrix regularization for the wrapped membrane on 10 ? S1 in the light-cone gauge. We give a concrete representation for the algebra and obtain the matrix string theory having the boundary conditions for the matrix variables corresponding to the wrapped membrane, which is referred to neither Seiberg and Sen's arguments nor string dualities. We also embed the configuration of the multi-wrapped membrane in matrix string theory.

Topological field theory for p-wave superconductors

Abstract: We propose a topological field theory for a spinless two-dimensional (2D) chiral superconductor (SC) that contains fundamental Majorana fields. Due to a fermionic gauge symmetry, the Majorana modes survive as dynamical degrees of freedom only at magnetic vortex cores, and on edges. We argue that these modes have the topological properties pertinent to a p-wave SC including the non-Abelian braiding statistics, and we support this claim by calculating the ground state degeneracy on a torus. We also briefly discuss the connection to the Moore-Read Pfaffian quantum Hall state and extensions to the spinfull case and to 3D topological SCs.