Construction of instantons

Atiyah, Michael; Hitchin, Nigel; Drinfeld, Vladimir; Manin, Yu. I.

doi:10.1016/0375-9601(78)90141-x

Cited by 1,362 publications

(1,545 citation statements)

References 2 publications

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“…The Ω-deformed theory has two additional complex parameters ε = (ε 1 , ε 2 ) which belong to the Cartan subalgebra of G rot C , ε ∈ LieT C Grot ≈ C 2 . In [101] we shall discuss the modification of the ADHM construction [8] producing the moduli spaces M γ (n, k) (cf. [77,88]) and the obstruction sheaf.…”

Section: Instanton Partition Functionmentioning

confidence: 99%

BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters

Nekrasov

2016

J. High Energ. Phys.

209

466

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We study symmetries of quantum field theories involving topologically distinct sectors of the field space. To exhibit these symmetries we define special gauge invariant observables, which we call the qq-characters. In the context of the BPS/CFT correspondence, using these observables, we derive an infinite set of Dyson-Schwinger-type relations. These relations imply that the supersymmetric partition functions in the presence of Ω-deformation and defects obey the Ward identities of two dimensional conformal field theory and its q-deformations. The details will be discussed in the companion papers.

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Section: Instanton Partition Functionmentioning

confidence: 99%

BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters

Nekrasov

2016

J. High Energ. Phys.

209

466

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“…The zero-modes are easily obtained by dimensionally reducing the maximally supersymmetric gauge theory to zero dimensions. We will use an ADHM [23] inspired notation [5,6]. We denote the bosonic fields as a µ and χ a , where the distinction between the two is made by the presence of the D3-branes.…”

Section: Preliminariesmentioning

confidence: 99%

Stringy instantons at orbifold singularities

Argurio

Bertolini

Ferretti

et al. 2007

J. High Energy Phys.

118

184

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Abstract:We study the effects produced by D-brane instantons on the holomorphic quantities of a D-brane gauge theory at an orbifold singularity. These effects are not limited to reproducing the well known contributions of the gauge theory instantons but also generate extra terms in the superpotential or the prepotential. On these brane instantons there are some neutral fermionic zero-modes in addition to the ones expected from broken supertranslations. They are crucial in correctly reproducing effects which are dual to gauge theory instantons, but they may make some other interesting contributions vanish. We analyze how orientifold projections can remove these zero-modes and thus allow for new superpotential terms. These terms contribute to the dynamics of the effective gauge theory, for instance in the stabilization of runaway directions.

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“…This is the situation considered in Section 4.2 for k = 2 and the generalization to k > 2 is reasonably straightforward. We focus on topicons of flavour v. Integrating over the fluctuations {w uiα , µ A ui ,μ A iu }, u = v produces the factor 22) where λ i are the eigenvalues of the k × k matrix χ. The remaining integral is then…”

Section: Arbitrary Instanton Numbermentioning

confidence: 99%

Testing Seiberg–Witten theory to all orders in the instanton expansion

Hollowood

2002

Nuclear Physics B

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In the context of softly-broken N = 4 to N = 2 supersymmetric SU(N) gauge theory, we calculate using semi-classical instanton methods, the lowest order non-trivial terms in the mass expansion of the prepotential for all instanton number. We find exact agreement with Seiberg-Witten theory and thereby achieve the most powerful test yet of this theory. We also calculate the one-and two-instanton contributions completely and also find consistency with Seiberg-Witten theory. Our approach relies on the fact that the instanton calculus admits a nilpotent fermionic symmetry, or BRST operator, whose existence implies that the integrals over the instanton moduli space, which give the coefficients of the prepotential, localize on the space of resolved point-like instantons or what we call "topicons".

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Construction of instantons

Cited by 1,362 publications

References 2 publications

BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters

BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters

Stringy instantons at orbifold singularities

Testing Seiberg–Witten theory to all orders in the instanton expansion

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