The Nekrasov Conjecture for Toric Surfaces

Gasparim, Elizabeth; Liu, Chiu-Chu Melissa

doi:10.1007/s00220-009-0948-4

Cited by 40 publications

(50 citation statements)

References 25 publications

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“…Theories of instantons and their moduli spaces are often defined over noncompact manifolds, as is the case with the instanton partition function, defined by Nekrasov [31] and explored by various authors, for instance [32,29,17,10].…”

Section: Motivationmentioning

confidence: 99%

Classical deformations of noncompact surfaces and their moduli of instantons

Barmeier

Gasparim

2019

Journal of Pure and Applied Algebra

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We describe semiuniversal deformation spaces for the noncompact surfaces Z k := Tot(O P 1 (−k)) and prove that any nontrivial deformation Z k (τ ) of Z k is affine.It is known that the moduli spaces of instantons of charge j on Z k are quasi-projective varieties of dimension 2j − k − 2. In contrast, our results imply that the moduli spaces of instantons on any nontrivial deformation Z k (τ ) are empty.

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Section: Motivationmentioning

confidence: 99%

Classical deformations of noncompact surfaces and their moduli of instantons

Barmeier

Gasparim

2019

Journal of Pure and Applied Algebra

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“…A natural class of complex surfaces X on which these considerations may be extended consists of orbifolds of C 2 and their resolutions. We begin by describing ALE spaces of type A k−1 regarded as toric varieties, following [51,30,26]; in this paper all cones are understood to be strictly convex rational polyhedral cones in a real vector space. For any non-negative integer i, define the lattice vector in L by…”

Section: Toric Geometry Of Ale Spacesmentioning

confidence: 99%

N=2 gauge theories, instanton moduli spaces and geometric representation theory

Szabo

2016

Journal of Geometry and Physics

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We survey some of the AGT relations between N = 2 gauge theories in four dimensions and geometric representations of symmetry algebras of two-dimensional conformal field theory on the equivariant cohomology of their instanton moduli spaces. We treat the cases of gauge theories on both flat space and ALE spaces in some detail, and with emphasis on the implications arising from embedding them into supersymmetric theories in six dimensions. Along the way we construct new toric noncommutative ALE spaces using the general theory of complex algebraic deformations of toric varieties, and indicate how to generalise the construction of instanton moduli spaces. We also compute the equivariant partition functions of topologically twisted six-dimensional Yang-Mills theory with maximal supersymmetry in a general Ω-background, and use the construction to obtain novel reductions to theories in four dimensions.

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“…We then consider instanton counting in the resolved spaces in §3. In §3.1 we first focus on the resolved A 1 -ALE space since the instanton counting scheme for this space has been rigorously established [4,5,6,7,8,9]. 1 In §3.2 we analyze the resolved A p−1 spaces with general p ≥ 2 by applying the physically motivated method developed in [11].…”

Section: Introductionmentioning

confidence: 99%

Scheme dependence of instanton counting in ALE spaces

Ito

Maruyoshi

Okuda

2013

J. High Energ. Phys.

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There have been two distinct schemes studied in the literature for instanton counting in A p−1 asymptotically locally Euclidean (ALE) spaces. We point out that the two schemes-namely the counting of orbifolded instantons and instanton counting in the resolved space-lead in general to different results for partition functions. We illustrate this observation in the case of N = 2 U (N ) gauge theory with 2N flavors on the A p−1 ALE space. We propose simple relations between the instanton partition functions given by the two schemes and test them by explicit calculations.

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The Nekrasov Conjecture for Toric Surfaces

Cited by 40 publications

References 25 publications

Classical deformations of noncompact surfaces and their moduli of instantons

Classical deformations of noncompact surfaces and their moduli of instantons

N=2 gauge theories, instanton moduli spaces and geometric representation theory

Scheme dependence of instanton counting in ALE spaces

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