Quantum Geometry and Quiver Gauge Theories

Abstract:We study the realization of supergroup gauge theories using negative branes in string theory. We show that negative branes are intimately connected with the possibility of timelike compactification and exotic spacetime signatures previously studied by Hull. Isolated negative branes dynamically generate a change in spacetime signature near their worldvolumes, and are related by string dualities to a smooth M-theory geometry with closed timelike curves. Using negative D3-branes, we show that SU(0|N ) supergroup theories are holographically dual to an exotic variant of type IIB string theory on dS 3,2 ×S 5 , for which the emergent dimensions are timelike. Using branes, mirror symmetry and Nekrasov's instanton calculus, all of which agree, we derive the Seiberg-Witten curve for N = 2 SU(N |M ) gauge theories. Together with our exploration of holography and string dualities for negative branes, this suggests that supergroup gauge theories may be non-perturbatively well-defined objects, though several puzzles remain.

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“…The SW curve for the SU(N ) × SU(N ) with two bi-fundamental matter fields has been worked out in [50] (see (7.81)) and was found to be:…”

Section: Instanton Calculusmentioning

confidence: 99%

Negative branes, supergroups and the signature of spacetime

Dijkgraaf

Heidenreich

Jefferson

et al. 2018

J. High Energ. Phys.

214

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“…The higher instanton corrections can be efficiently computed using localization methods [66][67][68][69], but their expressions will not be needed in the following. Inserting (7.9) into (7.7) and systematically working order by order in Λ N , it is possible to show that the N roots of the chiral ring equation (7.6) are…”

Section: Jhep07(2017)068mentioning

confidence: 99%

Modular and duality properties of surface operators in N = 2 ⋆ $$ \mathcal{N}={2}^{\star } $$ gauge theories

Ashok

Billó

Dell’Aquila

et al. 2017

J. High Energ. Phys.

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Abstract:We calculate the instanton partition function of the four-dimensional N = 2 ⋆ SU(N ) gauge theory in the presence of a generic surface operator, using equivariant localization. By analyzing the constraints that arise from S-duality, we show that the effective twisted superpotential, which governs the infrared dynamics of the two-dimensional theory on the surface operator, satisfies a modular anomaly equation. Exploiting the localization results, we solve this equation in terms of elliptic and quasi-modular forms which resum all non-perturbative corrections. We also show that our results, derived for monodromy defects in the four-dimensional theory, match the effective twisted superpotential describing the infrared properties of certain two-dimensional sigma models coupled either to pure N = 2 or to N = 2 ⋆ gauge theories.

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“…Recall that the Seiberg-Witten curve of the quiver gauge theory on the D5 branes is the spectral curve of the Higgs field φ, taken in some representation R of g ( [30][31][32]). We described the m s to infinity limit after which the Seiberg-Witten curve of the theory becomes the spectral curve of the Hitchin integrable system det R (φ − p) = 0.…”

Section: Parabolic Subalgebras From Higgs Field Datamentioning

confidence: 99%

Little string origin of surface defects

Haouzi

Schmid

2017

J. High Energ. Phys.

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We derive a large class of codimension-two defects of 4d N = 4 Super YangMills (SYM) theory from the (2, 0) little string. The origin of the little string is type IIB theory compactified on an ADE singularity. The defects are D-branes wrapping the 2-cycles of the singularity. We use this construction to make contact with the description of SYM defects due to Gukov and Witten [1]. Furthermore, we provide a geometric perspective on the nilpotent orbit classification of codimension-two defects, and the connection to ADEtype Toda CFT. The only data needed to specify the defects is a set of weights of the algebra obeying certain constraints, which we give explicitly. We highlight the differences between the defect classification in the little string theory and its (2, 0) CFT limit.

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Quantum Geometry and Quiver Gauge Theories

Cited by 150 publications

References 215 publications

Negative branes, supergroups and the signature of spacetime

Negative branes, supergroups and the signature of spacetime

Modular and duality properties of surface operators in N = 2 ⋆ $$ \mathcal{N}={2}^{\star } $$ gauge theories

Little string origin of surface defects

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