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326
Superstrings and topological strings at large
 N”, J. Math. Phys
"... We embed the large N ChernSimons/topological string duality in ordinary superstrings. This corresponds to a large N duality between generalized gauge systems with N = 1 supersymmetry in 4 dimensions and superstrings propagating on noncompact CalabiYau manifolds with certain fluxes turned on. We a ..."
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Cited by 214 (21 self)
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We embed the large N ChernSimons/topological string duality in ordinary superstrings. This corresponds to a large N duality between generalized gauge systems with N = 1 supersymmetry in 4 dimensions and superstrings propagating on noncompact CalabiYau manifolds with certain fluxes turned on. We also show that in a particular limit of the N = 1 gauge theory system, certain superpotential terms in the N = 1 system (including deformations if spacetime is noncommutative) are captured to all orders in 1/N by the amplitudes of noncritical bosonic strings propagating on a circle with selfdual radius. We also consider Dbrane/antiDbrane system wrapped over vanishing cycles of compact CalabiYau manifolds and argue that at large N they induce a shift in the background to a topologically distinct CalabiYau, which we identify as the ground state system of the Brane/antiBrane system. August
Two dimensional gauge theories revisited
 J. Geom. Phys
, 1992
"... Two dimensional quantum YangMills theory is reexamined using a nonabelian version of the DuistermaatHeckman integration formula to carry out the functional integral. This makes it possible to explain properties of the theory that are inaccessible to standard methods and to obtain general expressi ..."
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Cited by 150 (3 self)
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Two dimensional quantum YangMills theory is reexamined using a nonabelian version of the DuistermaatHeckman integration formula to carry out the functional integral. This makes it possible to explain properties of the theory that are inaccessible to standard methods and to obtain general expressions for intersection pairings on moduli spaces of flat connections on a two dimensional surface. The latter expressions agree, for gauge group SU(2), with formulas obtained recently by several methods. This paper will be devoted to a renewed study of two dimensional YangMills theory without matter, a system which can be easily solved [1] and has been extensively studied [2–10]. Yet we will see that there is still much to say about this supposedly “trivial ” system. To state our result in a nutshell, we will explain (in
Hodge integrals and GromovWitten theory
 Invent. Math
"... Let Mg,n be the nonsingular moduli stack of genus g, npointed, DeligneMumford stable curves. For each marking i, there is an associated cotangent line bundle Li → Mg,n with fiber T ∗ C,pi over the moduli point [C, p1,...,pn]. Let ψi = c1(Li) ∈ H ∗ (Mg,n, Q). The integrals of products of the ψ cla ..."
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Cited by 118 (12 self)
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Let Mg,n be the nonsingular moduli stack of genus g, npointed, DeligneMumford stable curves. For each marking i, there is an associated cotangent line bundle Li → Mg,n with fiber T ∗ C,pi over the moduli point [C, p1,...,pn]. Let ψi = c1(Li) ∈ H ∗ (Mg,n, Q). The integrals of products of the ψ classes
Lectures on 2D YangMills Theory, Equivariant Cohomology and Topological Field Theories
, 1996
"... These are expository lectures reviewing (1) recent developments in twodimensional YangMills theory and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of infinitedimensional differential geometry. We emphasize the unifying ..."
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Cited by 97 (7 self)
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These are expository lectures reviewing (1) recent developments in twodimensional YangMills theory and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of infinitedimensional differential geometry. We emphasize the unifying role of equivariant cohomology both as the underlying principle in the formulation of BRST transformation laws and as a central concept in the geometrical interpretation of topological field theory path integrals.
Intersection theory, integrable hierarchies and topological field theory
, 1992
"... In these lecture notes we review the various relations between intersection theory on the moduli space of Riemann surfaces, integrable hierarchies of KdV type, matrix models, and topological field theory. We focus in particular on the question why matrix integrals of the type considered by Kontsevic ..."
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Cited by 95 (5 self)
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In these lecture notes we review the various relations between intersection theory on the moduli space of Riemann surfaces, integrable hierarchies of KdV type, matrix models, and topological field theory. We focus in particular on the question why matrix integrals of the type considered by Kontsevich naturally appear as τfunctions of integrable hierarchies related to topological minimal models.
GromovWitten invariants and quantization of quadratic Hamiltonians
, 2001
"... We describe a formalism based on quantization of quadratic hamiltonians and symplectic actions of loop groups which provides a convenient home for most of known general results and conjectures about GromovWitten invariants of compact symplectic manifolds and, more generally, Frobenius structures at ..."
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Cited by 87 (3 self)
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We describe a formalism based on quantization of quadratic hamiltonians and symplectic actions of loop groups which provides a convenient home for most of known general results and conjectures about GromovWitten invariants of compact symplectic manifolds and, more generally, Frobenius structures at higher genus. We state several results illustrating the formalism and its use. In particular, we establish Virasoro constraints for semisimple Frobenius structures and outline a proof of the Virasoro conjecture for Gromov – Witten invariants of complex projective spaces and other Fano toric manifolds. Details will be published elsewhere.
Hurwitz numbers and intersections on moduli spaces of curves
 Invent. Math
"... 1.1. Topological classification of ramified coverings of the sphere. For a compact connected genus g complex curve C let f: C → CP 1 be a meromorphic function. We treat this function as a ramified covering of the sphere. Two ramified coverings (C1; f1), (C2; f2) are called topologically ..."
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Cited by 74 (2 self)
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1.1. Topological classification of ramified coverings of the sphere. For a compact connected genus g complex curve C let f: C → CP 1 be a meromorphic function. We treat this function as a ramified covering of the sphere. Two ramified coverings (C1; f1), (C2; f2) are called topologically
Bihamiltonian Hierarchies in 2D Topological Field Theory At OneLoop Approximation
, 1997
"... We compute the genus one correction to the integrable hierarchy describing coupling to gravity of a 2D topological field theory. The bihamiltonian structure of the hierarchy is given by a classical Walgebra; we compute the central charge of this algebra. We also express the generating function of ..."
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Cited by 73 (8 self)
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We compute the genus one correction to the integrable hierarchy describing coupling to gravity of a 2D topological field theory. The bihamiltonian structure of the hierarchy is given by a classical Walgebra; we compute the central charge of this algebra. We also express the generating function of elliptic Gromov Witten invariants via taufunction of the isomonodromy deformation problem arising in the theory of WDVV equations of associativity.
Higher genus symplectic invariants and sigma model coupled with gravity
"... This paper is a continuation of our previous paper [RT]. In [RT], among other things, we build up the mathematical foundation of quantum cohomology ring on semipositive symplectic manifolds. ..."
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Cited by 72 (7 self)
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This paper is a continuation of our previous paper [RT]. In [RT], among other things, we build up the mathematical foundation of quantum cohomology ring on semipositive symplectic manifolds.