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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, it was shown that topological A-model string amplitudes for toric Calabi-Yau 3-folds in non self-dual graviphoton background can be caluculated by a diagrammatic method that is called the ''refined topological vertex''.
Abstract: It has been proposed recently that topological A-model string amplitudes for toric Calabi-Yau 3-folds in non self-dual graviphoton background can be caluculated by a diagrammatic method that is called the ``refined topological vertex''. We compute the extended A-model amplitudes for SU(N)-geometries using the proposed vertex. If the refined topological vertex is valid, these computations should give rise to the Nekrasov's partition functions of = 2 SU(N) gauge theories via the geometric engineering. In this article, we verify the proposal by confirming the equivalence between the refined A-model amplitude and the K-theoretic version of the Nekrasov's partition function by explicit computation.
157 citations
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TL;DR: In this article, the authors describe sewing conditions in two-dimensional open/closed topological field theory, and give uniform proofs of all relevant sewing theorems using Morse theory.
Abstract: This expository paper describes sewing conditions in two-dimensional open/closed topological field theory. We include a description of the G-equivariant case, where G is a finite group. We determine the category of boundary conditions in the case that the closed string algebra is semisimple. In this case we find that sewing constraints – the most primitive form of worldsheet locality – already imply that D-branes are (G-twisted) vector bundles on spacetime. We comment on extensions to cochain-valued theories and various applications. Finally, we give uniform proofs of all relevant sewing theorems using Morse theory.
157 citations
TL;DR: In this paper, it was shown that the Gopakumar-Vafa invariants for these geometries to all orders in the fiber wrappings allow us to take the field theory limit.
Abstract: It has been conjectured recently that the field theory limit of the topological string partition functions, including all higher genus contributions, for the family of CY3folds giving rise to N = 2 4D SU(N) gauge theory via geometric engineering can be obtained from gauge instanton calculus. We verify this surprising conjecture by calculating the partition functions for such local CYs using diagrammatic techniques inspired by geometric transitions. Determining the Gopakumar-Vafa invariants for these geometries to all orders in the fiber wrappings allows us to take the field theory limit.
156 citations
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TL;DR: In this paper, a supersymmetric boundary interaction in N = 2 field theories on the half-space is constructed, which depend on parameters that are not at all renormalized or not renormalised in perturbation theory beyond one-loop.
Abstract: We construct a class of supersymmetric boundary interactions in N=2 field theories on the half-space, which depend on parameters that are not at all renormalized or not renormalized in perturbation theory beyond one-loop. This can be used to study D-branes wrapped on a certain class of Lagrangian submanifolds as well as holomorphic cycles. The construction of holomorphic D-branes is in close relationship with the background independent open string field theory approach to brane/anti-brane systems. As an application, mirror pairs of Lagrangian and holomorphic D-branes are identified. The mirror pairs are studied by twisting to open topological field theories.
155 citations
TL;DR: In this paper, a topological string theory was proposed which reproduces many aspects of the 1/N expansion of SU(N) Yang-Mills theory in two spacetime dimensions in the zero coupling (A= 0) limit.
Abstract: We describe a topological string theory which reproduces many aspects of the 1/N expansion of SU(N) Yang-Mills theory in two spacetime dimensions in the zero coupling (A= 0) limit. The string theory is a modified version of topological gravity coupled to a topological sigma model with spacetime as target. The derivation of the string theory relies on a new interpretation of Gross and Taylor's “Ω-1 points ”. We describe how inclusion of the area, coupling of chiral sectors, and Wilson loop expectation values can be incorporated in the topological string approach.
151 citations