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.

Recent developments in topological string theory

Abstract: This review summarizes the recent developments in topological string theory from the author’s perspective, mostly focusing on aspects of research in which the author is involved. After a brief overview of the theory, we discuss two aspects of these developments. First, we discuss the computational progress in the topological string partition functions on a class of elliptic Calabi-Yau manifolds. We propose to use Jacobi forms as an ansatz for the partition function. For non-compact models, the techniques often provide complete solutions, while for compact models, though it is still not completely solvable, we compute to higher genus than previous works. Second, we explore a remarkable connection of refined topological strings on a class of non-compact toric Calabi-Yau threefolds with non-perturbative effects in quantum-mechanical systems. The connections provide rarely available exact quantization conditions for quantum systems and new insights on non-perturbative formulations of topological string theory.

Spacetime Diffeomorphisms and Topological W-Infinity Symmetry in Two Dimensional Topological String Theory

Abstract: 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 $\Delta$ 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 $w_\infty$ at ghost number zero, and to a topologically twisted N=2 $w_\infty$ 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 $w_\infty$ superalgebra may emerge, while the semirelative cohomology leads to a bosonic $w_\infty$ symmetry.

Bulk Deformations of Open Topological String Theory

Abstract: We present a general method to construct bulk-deformed open topological string theories from Landau-Ginzburg models. To this end we obtain a weak version of deformation quantisation, and we show how this together with the technique of homological perturbation allows to explicitly compute all bulk-deformed open topological string amplitudes at tree-level before tadpole-cancellation. Our approach is based on a coherent treatment of the problem in terms of the fundamental A∞- and L∞-structures involved.