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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, the conjectured relation between the topological B-model and the Hitchin functional is studied at one loop, and the dependence of the one-loop result on a background metric is studied.
Abstract: The quantization in quadratic order of the Hitchin functional, which defines by critical points a Calabi–Yau structure on a six-dimensional manifold, is performed. The conjectured relation between the topological B-model and the Hitchin functional is studied at one loop. It is found that the genus one free energy of the topological B-model disagrees with the one-loop free energy of the minimal Hitchin functional. However, the topological B-model does agree at one-loop order with the extended Hitchin functional, which also defines by critical points a generalized Calabi–Yau structure. The dependence of the one-loop result on a background metric is studied, and a gravitational anomaly is found for both the B-model and the extended Hitchin model. The anomaly reduces to a volume-dependent factor if one computes for only Ricci-flat Kahler metrics
88 citations
TL;DR: In this article, the authors present a detailed description of the three inequivalent twists of N = 4 supersymmetric gauge theories in four dimensions and the resulting topological quantum field theories are reobtained in the framework of the Mathai-Quillen formalism.
88 citations
TL;DR: In this article, it was shown that the holomorphic anomaly equations in topological string theory reflect the quantum mechanical nature of the topological partition function, and that the general solution of the anomaly equations is a matrix element Ψ|g|Ω of the Schrodinger-Weil representation of a Heisenberg extension of G, between an arbitrary state Ω| and a particular vacuum state |Ω.
Abstract: It is generally known that the holomorphic anomaly equations in topological string theory reflect the quantum mechanical nature of the topological string partition function. We present two new results which make this assertion more precise: (i) we give a new, purely holomorphic version of the holomorphic anomaly equations, clarifying their relation to the heat equation satisfied by the Jacobi theta series; (ii) in cases where the moduli space is a Hermitian symmetric tube domain G/K, we show that the general solution of the anomaly equations is a matrix element Ψ|g|Ω of the Schrodinger-Weil representation of a Heisenberg extension of G, between an arbitrary state Ψ| and a particular vacuum state |Ω. Based on these results, we speculate on the existence of a one-parameter generalization of the usual topological amplitude, which in symmetric cases transforms in the smallest unitary representation of the duality group G' in three dimensions, and on its relations to hypermultiplet couplings, nonabelian Donaldson-Thomas theory and black hole degeneracies.
86 citations
TL;DR: In this article, a topological field theory for three-dimensional time-reversal invariant topological superconductors is presented, which predicts the level crossing induced by the crossing of special ''chiral'' vortex lines.
Abstract: Topological superconductors are gapped superconductors with gapless and topologically robust quasiparticles propagating on the boundary. In this paper, we present a topological field theory description of three-dimensional time-reversal invariant topological superconductors. In our theory the topological superconductor is characterized by a topological coupling between the electromagnetic field and the superconducting phase fluctuation, which has the same form as the coupling of ``axions'' with an Abelian gauge field. As a physical consequence of our theory, we predict the level crossing induced by the crossing of special ``chiral'' vortex lines, which can be realized by considering $s$-wave superconductors in proximity with the topological superconductor. Our theory can also be generalized to the coupling with a gravitational field.
85 citations
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TL;DR: The refined Chern-Simons theory and large N duality can be used to study the refined topological string with and without branes in this paper, and the result is suggestive of the refined vertex formalism for arbitrary toric Calabi-Yau manifolds in terms of a pair of vertices.
Abstract: We show that refined Chern-Simons theory and large N duality can be used to study the refined topological string with and without branes We derive the refined topological vertex of hep-th/0701156 and hep-th/0502061 from a link invariant of the refined SU(N) Chern-Simons theory on S^3, at infinite N Quiver-like Chern-Simons theories, arising from Calabi-Yau manifolds with branes wrapped on several minimal S^3's, give a dual description of a large class of toric Calabi-Yau We use this to derive the refined topological string amplitudes on a toric Calabi-Yau containing a shrinking P^2 surface The result is suggestive of the refined topological vertex formalism for arbitrary toric Calabi-Yau manifolds in terms of a pair of vertices and a choice of a Morse flow on the toric graph, determining the vertex decomposition The dependence on the flow is reminiscent of the approach to the refined topological string in upcoming work of Nekrasov and Okounkov As a byproduct, we show that large N duality of the refined topological string explains the ``mirror symmetry`` of the refined colored HOMFLY invariants of knots
85 citations