Results 1  10
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99
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.
Holomorphic triangles and invariants for smooth fourmanifolds
"... Abstract. The aim of this article is to introduce invariants of oriented, smooth, closed fourmanifolds, built using the Floer homology theories defined in [8] and [12]. This fourdimensional theory also endows the corresponding threedimensional theories with additional structure: an absolute gradi ..."
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Cited by 76 (24 self)
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Abstract. The aim of this article is to introduce invariants of oriented, smooth, closed fourmanifolds, built using the Floer homology theories defined in [8] and [12]. This fourdimensional theory also endows the corresponding threedimensional theories with additional structure: an absolute grading of certain of its Floer homology groups. The cornerstone of these constructions is the study of holomorphic disks in the symmetric products of Riemann surfaces. 1.
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.
Gauge theory for embedded surfaces
 I, Topology
, 1993
"... (i) Topology of embedded surfaces. Let X be a smooth, simplyconnected 4manifold, and ξ a 2dimensional homology class in X. One of the features of topology in dimension 4 is the fact that, although one may always represent ξ as the fundamental class of some smoothly ..."
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Cited by 68 (6 self)
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(i) Topology of embedded surfaces. Let X be a smooth, simplyconnected 4manifold, and ξ a 2dimensional homology class in X. One of the features of topology in dimension 4 is the fact that, although one may always represent ξ as the fundamental class of some smoothly
Supersymmetric Yang–Mills theory on a fourmanifold
 Jour. Math. Phys
, 1994
"... By exploiting standard facts about N = 1 and N = 2 supersymmetric YangMills theory, the Donaldson invariants of fourmanifolds that admit a Kahler metric can be computed. The results are in agreement with available mathematical computations, and provide a powerful check on the standard claims about ..."
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Cited by 67 (4 self)
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By exploiting standard facts about N = 1 and N = 2 supersymmetric YangMills theory, the Donaldson invariants of fourmanifolds that admit a Kahler metric can be computed. The results are in agreement with available mathematical computations, and provide a powerful check on the standard claims about supersymmetric YangMills theory. In fourdimensional supersymmetric YangMills theory formulated on flat R4, certain correlation functions are independent of spatial separation and are hence effectively computable by going to short distances. This is the basis for one of the most fruitful techniques for studying dynamics of those theories [1,2], and
Monopoles and four manifolds
 Math.Res. Lett
, 1994
"... Recent developments in the understanding of N = 2 supersymmetric YangMills theory in four dimensions suggest a new point of view about Donaldson theory of four manifolds: instead of defining fourmanifold invariants by counting SU(2) instantons, one can define equivalent fourmanifold invariants by ..."
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Cited by 67 (2 self)
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Recent developments in the understanding of N = 2 supersymmetric YangMills theory in four dimensions suggest a new point of view about Donaldson theory of four manifolds: instead of defining fourmanifold invariants by counting SU(2) instantons, one can define equivalent fourmanifold invariants by counting solutions of a nonlinear equation with an abelian gauge group. This is a “dual ” equation in which the gauge group is the dual of the maximal torus of SU(2). The new viewpoint suggests many new results about the Donaldson invariants. November
TOPOLOGICAL FIELD THEORY AND RATIONAL CURVES
, 1991
"... We analyze the quantum field theory corresponding to a string propagating on a CalabiYau threefold. This theory naturally leads to the consideration of Witten’s topological nonlinear σmodel and the structure of rational curves on the CalabiYau manifold. We study in detail the case of the world ..."
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Cited by 62 (6 self)
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We analyze the quantum field theory corresponding to a string propagating on a CalabiYau threefold. This theory naturally leads to the consideration of Witten’s topological nonlinear σmodel and the structure of rational curves on the CalabiYau manifold. We study in detail the case of the worldsheet of the string being mapped to a multiple cover of an isolated rational curve and we show that a natural compactification of the moduli space of such a multiple cover leads to a formula in agreement with a conjecture by Candelas, de la Ossa, Green and Parkes.
K3 surfaces and string duality
"... The primary purpose of these lecture notes is to explore the moduli space of type IIA, type IIB, and heterotic string compactified on a K3 surface. The main tool which is invoked is that of string duality. K3 surfaces provide a fascinating arena for string compactification as they are not trivial sp ..."
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Cited by 62 (14 self)
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The primary purpose of these lecture notes is to explore the moduli space of type IIA, type IIB, and heterotic string compactified on a K3 surface. The main tool which is invoked is that of string duality. K3 surfaces provide a fascinating arena for string compactification as they are not trivial spaces but are sufficiently simple for one to be able to analyze most of their properties in detail. They also make an almost ubiquitous appearance in the common statements concerning string duality. We review the necessary facts concerning the classical geometry of K3 surfaces that will be needed and then we review “old string theory ” on K3 surfaces in terms of conformal field theory. The type IIA string, the type IIB string, the E8 × E8 heterotic string, and Spin(32)/Z2 heterotic string on a K3 surface are then each analyzed in turn. The discussion is biased in favour of purely geometric notions concerning the K3 surface