A mathematical theory of the gauged linear sigma model
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In this paper, a mathematical theory of Witten's GLSM is presented, which applies to a wide range of examples, including many cases with nonabelian gauge groups.Abstract:
We construct a mathematical theory of Witten’s Gauged Linear Sigma Model (GLSM). Our theory applies to a wide range of examples, including many cases with nonabelian gauge group. Both the Gromov–Witten theory of a Calabi–Yau complete intersection X and the Landau–Ginzburg dual (FJRW theory) of X can be expressed as gauged linear sigma models. Furthermore, the Landau–Ginzburg/Calabi–Yau correspondence can be interpreted as a variation of the moment map or a deformation of GIT in the GLSM. This paper focuses primarily on the algebraic theory, while a companion article will treat the analytic theory.read more
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Mixed-Spin-P fields of Fermat quintic polynomials
TL;DR: The first part of the project toward an effective algorithm to evaluate genus Gromov-Witten invariants of quintic Calabi-Yau threefolds is described in this paper.
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A mirror theorem for genus two Gromov-Witten invariants of quintic threefolds
TL;DR: In this article, a closed formula for the generating function of genus two Gromov-Witten invariants of quintic 3-folds was derived and the corresponding mirror symmetry conjecture of Bershadsky, Cecotti, Ooguri and Vafa was verified.
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Fundamental Factorization of a GLSM, Part I: Construction
TL;DR: It is proved that in the relevant special cases, enumerative invariants associated to a hybrid Gauged Linear Sigma Model recover both the Gromov-Witten type invariants defined by Chang-Li and Fan-Jarvis-Ruan using cosection localization as well as the FJRW type invariant constructed by Polishchuk-Vaintrob.
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An Effective Theory of GW and FJRW Invariants of Quintics Calabi-Yau Manifolds
TL;DR: In this paper, the localization formula is derived, and algorithms toward evaluating these Gromov-Witten invariants are derived for the quintic Calabi-Yau threefold.
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The level structure in quantum K-theory and mock theta functions
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TL;DR: In this article, the theory of levels in quantum K-theory with level structure has been developed and applied to a variety of applications, such as Ramanujan's mock theta functions.
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Phases of N = 2 theories in two dimensions
TL;DR: In this paper, a natural relation between sigma models based on Calabi-Yau hypersurfaces in weighted projective spaces and Landau-Ginzburg models is found.
Journal ArticleDOI
Intersection theory on the moduli space of curves and the matrix Airy function
TL;DR: In this article, it was shown that two natural approaches to quantum gravity coincide, relying on the equivalence of each approach to KdV equations, and they also investigated related mathematical problems.
Book
Moduli of curves
Joe Harris,Ian Morrison +1 more
TL;DR: In this article, the Brill-Noether theory is applied to moduli spaces of curves of curves, and a technique for construction of M_g is described, based on the limit linear series and the Brill noether theory.
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