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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.
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TL;DR: In this paper, a direct relation between quiver representation theory and open topological string theory on a class of toric Calabi-Yau manifolds without compact four-cycles, referred to as strip geometries, was found.
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.
6 citations
Posted Content•
TL;DR: In this article, four-dimensional compactifications of type II superstrings on Calabi-Yau spaces using the formalism of hybrid string theory are studied, which involve coupling of the compactification moduli to two powers of the Weyl-tensor and of the derivative of the universal tensor field strength.
Abstract: We study four-dimensional compactifications of type II superstrings on Calabi-Yau spaces using the formalism of hybrid string theory. Chiral and twisted-chiral interactions are rederived, which involve the coupling of the compactification moduli to two powers of the Weyl-tensor and of the derivative of the universal tensor field-strength.
6 citations
TL;DR: In this paper, the moduli space constraint is introduced as a gauge fixing in the N = 2 Liouville model of constrained topological gravity, which is a generalization of the BRST algebra.
6 citations
Journal Article•
TL;DR: In this paper, it was shown that the all-orders WKB periods of one-dimensional quantum mechanical oscillators are governed by the refined holomorphic anomaly equations of topological string theory.
Abstract: We show that the all-orders WKB periods of one-dimensional quantum mechanical oscillators are governed by the refined holomorphic anomaly equations of topological string theory. We analyze in detail the double-well potential and the cubic and quartic oscillators, and we calculate the WKB expansion of their quantum free energies by using the direct integration of the anomaly equations. We reproduce in this way all known results about the quantum periods of these models, which we express in terms of modular forms on the WKB curve. As an application of our results, we study the large order behavior of the WKB expansion in the case of the double well, which displays the double factorial growth typical of string theory.
6 citations
TL;DR: In this article, the small-scale structure of a string connecting a pair of static sources is explored for the weakly-coupled anisotropic SU(2) Yang-Mills theory in (2+1) dimensions.
Abstract: The small-scale structure of a string connecting a pair of static sources is explored for the weakly-coupled anisotropic SU(2) Yang-Mills theory in (2+1) dimensions A crucial ingredient in the formulation of the string Hamiltonian is the phenomenon of color smearing of the string constituents The quark-anti-quark potential is determined We close with some discussion of the standard, fully Lorentz-invariant Yang-Mills theory
6 citations