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Superpotential
About: Superpotential is a research topic. Over the lifetime, 3836 publications have been published within this topic receiving 137867 citations.
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TL;DR: In this article, the authors carried out explicit calculations involving PO on toric manifolds and studied the relationship between this class of Lagrangian submanifolds with the earlier work of Givental [G1], which advocates that the quantum cohomology ring is isomorphic to the Jacobian ring of a certain function, called the Landau-Ginzburg superpotential.
Abstract: We introduced the notion of weakly unobstructed Lagrangian submanifolds and constructed their potential function (PO) purely in terms of A-model data in [FOOO3]. In this article, we carry out explicit calculations involving PO on toric manifolds and study the relationship between this class of Lagrangian submanifolds with the earlier work of Givental [G1], which advocates that the quantum cohomology ring is isomorphic to the Jacobian ring of a certain function, called the Landau-Ginzburg superpotential. Combining this study with the results from [FOOO3], we also apply the study to various examples to illustrate its implications to symplectic topology of Lagrangian fibers of toric manifolds. In particular, we relate it to the Hamiltonian displacement property of Lagrangian fibers and to Entov-Polterovich's symplectic quasi-states
206 citations
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TL;DR: In this paper, the topological string amplitudes of N = 1 and N = 2 supersymmetric gauge theories are derived from topological strings and used to check a conjecture of Nekrasov concerning these gravitational couplings in Seiberg-Witten theory.
Abstract: Gravitational corrections in N = 1 and N = 2 supersymmetric gauge theories are obtained from topological string amplitudes. We show how they are recovered in matrix model computations. This provides a test of the proposal by Dijkgraaf and Vafa beyond the planar limit. Both, matrix model and topological string theory, are used to check a conjecture of Nekrasov concerning these gravitational couplings in Seiberg-Witten theory. Our analysis is performed for those gauge theories which are related to the cubic matrix model, i.e. pure SU(2) Seiberg-Witten theory and N = 2 U(N) SYM broken to N = 1 via a cubic superpotential. We outline the computation of the topological amplitudes for the local Calabi-Yau manifolds which are relevant for these two cases.
206 citations
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TL;DR: In this paper, a local geometric model in terms of F-and M-theory compactification on Calabi-Yau 4-folds is constructed, which leads to N = 1 Yang-Mills theory in d = 4 and its reduction on a circle to d = 3.
206 citations
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TL;DR: Some general techniques for analyzing the Wilsonian superpotential are discussed and demonstrated with simple but nontrivial examples.
Abstract: Supersymmetric gauge theories in four dimensions can display interesting nonperturbative phenomena. Although the superpotential dynamically generated by these phenomena can be highly nontrivial, it can often be exactly determined. We discuss some general techniques for analyzing the Wilsonian superpotential and demonstrate them with simple but nontrivial examples.
205 citations
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TL;DR: In this article, the construction of realistic superstring standard-like models in the four-dimensional free fermionic formulation was discussed, and the analysis results in a restricted class of models with unique characteristics.
205 citations