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.

Tracing the string: BMN correspondence at finite J**2/N

Abstract: Employing the string bit formalism of [18], we identify the basis transformation that relates BMN operators in = 4 gauge theory to string states in the dual string field theory at finite g2 = J2/N. In this basis, the supercharge truncates at linear order in g2, and the mixing amplitude between 1 and 2-string states precisely matches with the (corrected) answer of [5] for the 3-string amplitude in light-cone string field theory. Supersymmetry then predicts the order g22 contact term in the string bit hamiltonian. The resulting leading order mass renormalization of string states agrees with the recently computed shift in conformal dimension of BMN operators in the gauge theory.

String field theory and brane superpotentials

Abstract: I discuss tree-level amplitudes in cubic topological string field theory, showing that a certain family of gauge conditions leads to an A∞ algebra of tree-level string products which define a potential describing the dynamics of physical states Upon using results of modern deformation theory, I show that the string moduli space admits two equivalent descriptions, one given in standard Maurer-Cartan fashion and another given in terms of a `homotopy Maurer-Cartan problem', which describes the critical set of the potential By applying this construction to the topological A and B models, I obtain an intrinsic formulation of `D-brane superpotentials' in terms of string field theory data This gives a prescription for computing such quantities to all orders, and proves the equivalence of this formulation with the fundamental description in terms of string field moduli In particular, it clarifies the relation between the Chern-Simons/holomorphic Chern-Simons actions and the superpotential for A/B-type branes

Direct integration for general Omega backgrounds

Abstract: We extend the direct integration method of the holomorphic anomaly equations to general Omega backgrounds for pure SU(2) N=2 Super-Yang-Mills theory and topological string theory on non-compact Calabi-Yau threefolds. We find that an extension of the holomorphic anomaly equation, modularity and boundary conditions provided by the perturbative terms as well as by the gap condition at the conifold are sufficient to solve the generalized theory in the above cases. In particular we use the method to solve the topological string for the general Omega backgrounds on non-compact toric Calabi-Yau spaces. The conifold boundary condition follows from that the N=2 Schwinger-Loop calculation with BPS states coupled to a self-dual and an anti-self-dual field strength. We calculate such BPS states also for the decompactification limit of Calabi-Yau spaces with regular K3 fibrations and half K3s embedded in Calabi-Yau backgrounds.