The omega deformation from string and M-theory

Hellerman, Simeon; Orlando, Domenico; Reffert, Susanne

doi:10.1007/jhep07(2012)061

Cited by 62 publications

(86 citation statements)

References 67 publications

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“…For this purpose, we have to consider the 10D conformal group SO(2, 10) and realize 10D Minkowski spacetime as a slice of 11D AdS space. We expect that in this case 10D supersymmetric configurations like the fluxtrap backgrounds [93][94][95][96] could be reproduced as Yang-Baxter deformations.…”

Section: Conclusion and Discussionmentioning

confidence: 91%

Yang-Baxter deformations of Minkowski spacetime

Matsumoto

Orlando

Reffert

et al. 2015

J. High Energ. Phys.

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We study Yang-Baxter deformations of 4D Minkowski spacetime. The YangBaxter sigma model description was originally developed for principal chiral models based on a modified classical Yang-Baxter equation. It has been extended to coset curved spaces and models based on the usual classical Yang-Baxter equation. On the other hand, for flat space, there is the obvious problem that the standard bilinear form degenerates if we employ the familiar coset Poincaré group/Lorentz group. Instead we consider a slice of AdS 5 by embedding the 4D Poincaré group into the 4D conformal group SO(2, 4) . With this procedure we obtain metrics and B-fields as Yang-Baxter deformations which correspond to well-known configurations such as T-duals of Melvin backgrounds, Hashimoto-Sethi and Spradlin-Takayanagi-Volovich backgrounds, the T-dual of Grant space, pp-waves, and T-duals of dS 4 and AdS 4 . Finally we consider a deformation with a classical r-matrix of Drinfeld-Jimbo type and explicitly derive the associated metric and B-field which we conjecture to correspond to a new integrable system.

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Section: Conclusion and Discussionmentioning

confidence: 91%

Yang-Baxter deformations of Minkowski spacetime

Matsumoto

Orlando

Reffert

et al. 2015

J. High Energ. Phys.

Self Cite

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“…It is in fact fairly ubiquitous, applicable even for nonconstant B-field. Its connection to T-duality has been exploited in actions that make nongeometric fluxes manifest [23,24] and string theory explanations [25,26] of the Ω-deformation [27,28]. More recently, it was noted [29,30] that the closed-open string map undoes integrable deformations of σ-models [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Classical Yang-Baxter equation from supergravity

et al. 2018

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We promote the open-closed string map, originally formulated by Seiberg & Witten, to a solution generating prescription in generalized supergravity. The approach hinges on a knowledge of an antisymmetric bivector Θ, built from antisymmetric products of Killing vectors, which is specified by the equations of motion. In the cases we study, the equations of motion reproduce the classical Yang-Baxter equation (CYBE) and Θ is the most general r-matrix solution. Our work generalizes Yang-Baxter deformations to non-coset spaces and unlocks gravity as a means to classify r-matrix solutions to the CYBE.

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“…With the introduction of the so-called Ω-background [5][6][7] and its interpretation in terms of Neveu-Schwarz/Neveu-Schwarz or Ramond/Ramond field strengths of closed string theory [8][9][10][11], the connection between the gauge theory prepotential and the topological string amplitudes has become more clear, and recently there has been a renewed interest both in computing such amplitudes [12][13][14][15][16] and in adapting the previous works to this new scenario [17][18][19][20][21]. In particular, in [19,21] the N = 2 * theory with gauge group SU (2) has been studied in a generic Ω-background characterized by two independent parameters, 1 and 2 , and its prepotential, including all its non-perturbative instanton corrections, has been computed in a small mass expansion.…”

Section: Jhep10(2014)131mentioning

confidence: 99%

“…Here we have defined 2 10) and introduced the sums 11) and an arbitrary scale Λ in the logarithmic term. The coefficients f 1−loop n 's for higher n have more complicated expressions but their dependence on the vacuum expectation values a i 's is entirely through the sums C n .…”

Section: The One-loop Prepotentialmentioning

confidence: 99%

Modular anomaly equations in N $$ \mathcal{N} $$ =2* theories and their large-N limit

Billó

Frau

Fucito

et al. 2014

J. High Energ. Phys.

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We propose a modular anomaly equation for the prepotential of the N = 2 * super Yang-Mills theory on R 4 with gauge group U(N ) in the presence of an Ω-background. We then study the behavior of the prepotential in a large-N limit, in which N goes to infinity with the gauge coupling constant kept fixed. In this regime instantons are not suppressed. We focus on two representative choices of gauge theory vacua, where the vacuum expectation values of the scalar fields are distributed either homogeneously or according to the Wigner semi-circle law. In both cases we derive an all-instanton exact formula for the prepotential. As an application, we show that the gauge theory partition function on S 4 at large N localizes around a Wigner distribution for the vacuum expectation values leading to a very simple expression in which the instanton contribution becomes independent of the coupling constant.

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The omega deformation from string and M-theory

Cited by 62 publications

References 67 publications

Yang-Baxter deformations of Minkowski spacetime

Yang-Baxter deformations of Minkowski spacetime

Classical Yang-Baxter equation from supergravity

Modular anomaly equations in N $$ \mathcal{N} $$ =2* theories and their large-N limit

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