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.

An Action for higher spin gauge theory in four dimensions

Abstract: An action principle is presented for Vasiliev's Bosonic higher spin gauge theory in four spacetime dimensions. The action is of the form of a broken topological field theory, and arises by an extension of the MacDowell-Mansouri formulation of general relativity. In the latter theory the local degrees of freedom of general relativity arise by breaking the gauge invariance of a topological theory from $sp(4)$ to the Lorentz algebra. In Vasiliev's theory the infinite number of degrees of freedom with higher spins similarly arise by the breaking of a topological theory with an infinite dimensional gauge symmetry extending $sp(4)$ to the Lorentz algebra. The Hamiltonian formulation of Vasilev's theory is then derived from our action, and it is shown that the Hamiltonian is a linear combination of constraints, as expected for a diffeomorphism invariant theory. The constraint algebra is computed and found to be first class.

The Self-Dual String and Anomalies in the M5-brane

Abstract: We study the anomalies of a charge $Q_2$ self-dual string solution in the Coulomb branch of $Q_5$ M5-branes Cancellation of these anomalies allows us to determine the anomaly of the zero-modes on the self-dual string and their scaling with $Q_2$ and $Q_5$ The dimensional reduction of the five-brane anomalous couplings then lead to certain anomalous couplings for D-branes

Topological Strings and QCD in Two Dimensions

Abstract: I present a new class of topological string theories, and discuss them in two dimensions as candidates for the string description of large-N QCD. The starting point is a new class of topological sigma models, whose path integral is localized to the moduli space of harmonic maps from the worldsheet to the target. The Lagrangian is of fourth order in worldsheet derivatives. After gauging worldsheet diffeomorphisms in this “harmonic topological sigma model,” we obtain a topological string theory dominated by minimal-area maps. The bosonic part of this “topological rigid string” Lagrangian coincides with the Lagrangian proposed by Polyakov for the QCD string in higher dimensions.

Topological strings, strips and quivers

Abstract: We find a direct relation between quiver representation theory and open topological string theory on a class of toric Calabi-Yau manifolds without compact four-cycles, also referred to as strip geometries. We show that various quantities that characterize open topological string theory on these manifolds, such as partition functions, Gromov-Witten invariants, or open BPS invariants, can be expressed in terms of characteristics of the moduli space of representations of the corresponding quiver. This has various deep consequences; in particular, expressing open BPS invariants in terms of motivic Donaldson-Thomas invariants, immediately proves integrality of the former ones. Taking advantage of the relation to quivers we also derive explicit expressions for classical open BPS invariants for an arbitrary strip geometry, which lead to a large set of number theoretic integrality statements. Furthermore, for a specific framing, open topological string partition functions for strip geometries take form of generalized q-hypergeometric functions, which leads to a novel representation of these functions in terms of quantum dilogarithms and integral invariants. We also study quantum curves and A-polynomials associated to quivers, various limits thereof, and their specializations relevant for strip geometries. The relation between toric manifolds and quivers can be regarded as a generalization of the knots-quivers correspondence to more general Calabi-Yau geometries.