Constraints For Topological Strings In $D\geq 1$
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In this article, new relations of correlation functions are found in topological string theory; one for each second cohomology class of the target space; and they are close cousins of the Deligne-Dijkgraaf-Witten's puncture and dilaton equations.Abstract:
New relations of correlation functions are found in topological string theory; one for each second cohomology class of the target space. They are close cousins of the Deligne-Dijkgraaf-Witten's puncture and dilaton equations. When combined with the dilaton equation and the ghost number conservation, the equation for the first chern class of the target space gives a constraint on the topological sum (over genera and (multi-)degrees) of partition functions. For the $\CP^1$ model, it coincides with the dilatation constraint which is derivable in the matrix model recently introduced by Eguchi and Yang.read more
Citations
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Book ChapterDOI
Painlevé Transcendents in Two-Dimensional Topological Field Theory
TL;DR: In this article, the theory of WDVV equations of associativity is studied, where the primary free energy of a family of two-dimensional topological field theories is derived as an efficient tool in the solution of problems of Gromov-Witten invariants, reflection groups and singularities.
Journal ArticleDOI
Instantons and merons in matrix models
TL;DR: In this article, a decomposition of matrix model partition functions is proposed, which is the matrix model version of multi-instanton and multi-meron configurations in Yang-Mills theories.
Journal ArticleDOI
Products of Floer Cohomology of Torus Fibers in Toric Fano Manifolds
TL;DR: In this paper, the ring structure of Floer cohomology groups of Lagrangian torus fibers in some toric Fano manifolds has been studied and it has been shown that these rings are isomorphic to Clifford algebras, whose quadratic forms are given by the Hessians of functions W, which turn out to be the superpotentials of Landau-Ginzburg mirrors.
Book ChapterDOI
The jet-space of a Frobenius manifold and higher-genus Gromov-Witten invariants
TL;DR: The theory of genus zero Gromov-Witten invariants associates to a compact symplectic manifold X a Frobenius manifold H (also known as the small phase space of X) whose underlying flat manifold is the cohomology space H*(X, ℂ) higher genus GromOV-Went invariants give rise to a sequence of generating functions F g X, one for each genus g > 0; these are functions on the large phase space ======¯¯¯¯\/\/\/\/\/\/
Journal ArticleDOI
Correlators in the simplest gauge-string duality
Rajesh Gopakumar,Roji Pius +1 more
TL;DR: In this article, the authors compare planar correlators such as the Gaussian matrix model with corresponding genus zero correlators of the A-model topological string theory and find a simple relation between them which provides additional evidence for the duality between the two theories.
References
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Phillip Griffiths,Joe Harris +1 more
TL;DR: In this paper, a comprehensive, self-contained treatment of complex manifold theory is presented, focusing on results applicable to projective varieties, and including discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex.
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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.
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Topological sigma models
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Gromov-Witten classes, quantum cohomology, and enumerative geometry
Maxim Kontsevich,Yu. I. Manin +1 more
TL;DR: In this article, the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry are discussed, and an axiomatic treatment of Gromov-Witten classes and their properties for Fano varieties are discussed.