The moment map and equivariant cohomology
TL;DR: In this article, the authors propose a solution to solve the problem of spamming, which is called spamming-based spamming.$$$/$/$/$/$$
About: This article is published in Topology.The article was published on 1984-01-01 and is currently open access. It has received 1294 citations till now. The article focuses on the topics: Equivariant cohomology & Equivariant map.
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TL;DR: In this article, a two-parameter generalization of the Seiberg-Witten prepotential is presented, which is rather natural from the M-theory/five dimensional perspective, and conjecture its relation to the tau-functions of KP/Toda hierarchy.
Abstract: Direct evaluation of the Seiberg-Witten prepotential is accomplished following the localization programme suggested in [1]. Our results agree with all low-instanton calculations available in the literature. We present a two-parameter generalization of the Seiberg-Witten prepotential, which is rather natural from the M-theory/five dimensional perspective, and conjecture its relation to the tau-functions of KP/Toda hierarchy.
2,159 citations
TL;DR: In this article, the authors proved conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators with a Gaussian matrix model.
Abstract: We prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the \({\mathcal N=4}\) supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure \({\mathcal N=2}\) and the \({\mathcal N=2^*}\) supersymmetric Yang-Mills theory on a four-sphere. A four-dimensional \({\mathcal N=2}\) superconformal gauge theory is treated similarly.
1,773 citations
Cites background or methods from "The moment map and equivariant coho..."
...Now recall Atiyah-Bott-Berline-Vergne localization formula for the integrals of the equivariantly closed differential forms [46, 47]...
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...The Duistermaat-Heckman formula is a particular case of a more general Atiyah-Bott-Berline-Vergne localization formula [46, 47]....
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01 Jan 2003
TL;DR: In this paper, a two-parameter generalization of the Seiberg-Witten prepotential is presented, which is rather natural from the M-theory/five dimensional perspective, and conjecture its relation to the tau-functions of KP/Toda hierarchy.
Abstract: Direct evaluation of the Seiberg-Witten prepotential is accomplished following the localization programme suggested in [1]. Our results agree with all low-instanton calculations available in the literature. We present a two-parameter generalization of the Seiberg-Witten prepotential, which is rather natural from the M-theory/five dimensional perspective, and conjecture its relation to the tau-functions of KP/Toda hierarchy.
1,215 citations
TL;DR: A variant of the usual supersymmetric nonlinear sigma model is described in this article, governing maps from a Riemann surface to an arbitrary almost complex manifold, which possesses a fermionic BRST-like symmetry, conserved for arbitrary Σ, and obeying Q 2 = 0.
Abstract: A variant of the usual supersymmetric nonlinear sigma model is described, governing maps from a Riemann surfaceΣ to an arbitrary almost complex manifoldM. It possesses a fermionic BRST-like symmetry, conserved for arbitraryΣ, and obeyingQ
2=0. In a suitable version, the quantum ground states are the 1+1 dimensional Floer groups. The correlation functions of the BRST-invariant operators are invariants (depending only on the homotopy type of the almost complex structure ofM) similar to those that have entered in recent work of Gromov on symplectic geometry. The model can be coupled to dynamical gravitational or gauge fields while preserving the fermionic symmetry; some observations by Atiyah suggest that the latter coupling may be related to the Jones polynomial of knot theory. From the point of view of string theory, the main novelty of this type of sigma model is that the graviton vertex operator is a BRST commutator. Thus, models of this type may correspond to a realization at the level of string theory of an unbroken phase of quantum gravity.
1,173 citations
Cites background from "The moment map and equivariant coho..."
...According to [19,20], this is the G-equivalent cohomology of M....
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TL;DR: In this paper, a stability condition for a polarised algebraic variety is defined and a conjecture relating this to the existence of a Kahler metric of constant scalar curvature.
Abstract: We define a stability condition for a polarised algebraic variety and state a conjecture relating this to the existence of a Kahler metric of constant scalar curvature. The main result of the paper goes some way towards verifying this conjecture in the case of toric surfaces. We prove that, under the stability hypothesis, the Mabuchi functional is bounded below on invariant metrics, and that minimising sequences have a certain convergence property. In the reverse direction, we give new examples of polarised surfaces which do not admit metrics of constant scalar curvature. The proofs use a general framework, developed by Guillemin and Abreu, in which invariant Kahler metrics correspond to convex functions on the moment polytope of a toric variety. This paper is a step towards the solution of the general problem of finding conditions under which a complex projective variety admits a Kahler metric of constant scalar curvature. The pattern of the answer one expects is that this differential geometric condition should be equivalent to some notion of “stability” in the sense of Geometric Invariant Theory. This expectation is probably now an item of folklore: going back to suggestions put forward by Yau in the case of KahlerEinstein metrics, and the many results of Tian and others in this case; reinforced by a detailed formal picture which makes clear the analogy with the well-established relation between the stability of vector bundles and Yang-Mills connections [5]. Here, we begin the investigation of
945 citations
Cites methods from "The moment map and equivariant coho..."
...To make the calculation we use the de Rham model of equivariant cohomology, with the complex ( ΩV0 )S1 [t] and differential d+tiv, see [2]....
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References
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Book•
01 Jan 1969
TL;DR: It is shown here how the Noetherian Rings and Dedekind Domains can be transformed into rings and Modules of Fractions using the following structures:
Abstract: * Introduction * Rings and Ideals * Modules * Rings and Modules of Fractions * Primary Decomposition * Integral Dependence and Valuations * Chain Conditions * Noetherian Rings * Artin Rings * Discrete Valuation Rings and Dedekind Domains * Completions * Dimension Theory
4,168 citations
"The moment map and equivariant coho..." refers background in this paper
...This can be done by passing to the field of fractions C(u,, . . . , uJ. If we want more precise information we must use some of the notions of commutative algebra (see for example Atiyah-Macdonald[ 3 ])....
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TL;DR: In this article, the Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory, and the main result is that this is a perfect 9 functional provided due account is taken of its gauge symmetry.
Abstract: The Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory. The main result is that this is a ‘perfect9 functional provided due account is taken of its gauge symmetry. This enables topological conclusions to be drawn about the critical sets and leads eventually to information about the moduli space of algebraic bundles over the Riemann surface. This in turn depends on the interplay between the holomorphic and unitary structures, which is analysed in detail.
2,298 citations
TL;DR: In this paper, it was shown that the Morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics Hamiltonian, and some of the implications of modern ideas in mathematics for super-ymmetric theories are discussed.
Abstract: It is shown that the Morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics Hamiltonian. Some of the implications of modern ideas in mathematics for supersymmetric theories are discussed.
1,625 citations
TL;DR: In this article, the adjoint action of G on its Lie algebra L(G) was considered and it was shown that W-orbits in L(T) correspond to G-orbit in L (G).
Abstract: The converse was proved by A. Horn [5], so that all points in this convex hull occur as diagonals of some matrix A with the given eigenvalues. Kostant [7] generalized these results to any compact Lie group G in the following manner. We consider the adjoint action of G on its Lie algebra L(G). If T is a maximal torus of G and W its Weyl group, then it is well known that W-orbits in L(T) correspond to G-orbits in L(G). Now fix a G-invariant metric on L(G), so that we can define orthogonal projection. Then Kostant's result isf
1,068 citations