Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter

Kapustin, Anton; Willett, Brian; Yaakov, Itamar

doi:10.48550/arxiv.0909.4559

Cited by 351 publications

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“…This provides a powerful method to compute the 1/N corrections at strong 't Hooft coupling in dual CFT's. In [7] the localization technique was applied to N = 6 U(N) k × U(N) −k Chern-Simons-matter theory, also known as the ABJM theory, dual to type IIA strings on AdS 4 × CP 3 or M-theory on AdS 4 × S 7 /Z k [8]. The partition function of the ABJM theory reduces to the eigenvalue integrals and this defines the ABJM matrix model.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Summing up all genus free energy of ABJM matrix model

Fuji

Hirano

Moriyama

2011

J. High Energ. Phys.

151

194

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The localization technique allows us to compute the free energy of the U (N ) k × U (N ) −k Chern-Simons-matter theory dual to type IIA strings on AdS 4 × CP 3 from weak to strong 't Hooft coupling λ = N/k at finite N , as demonstrated by Drukker, Mariño, and Putrov. In this note we study further the free energy at large 't Hooft coupling with the aim of testing AdS/CFT at the quantum gravity level and, in particular, sum up all the 1/N corrections, apart from the worldsheet instanton contributions. The all genus partition function takes a remarkably simple form -the Airy function, Ai (πk 2 / √ 2) 2/3 λ ren , with the renormalized 't Hooft coupling λ

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Summing up all genus free energy of ABJM matrix model

Fuji

Hirano

Moriyama

2011

J. High Energ. Phys.

151

194

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“…• In Coulomb branch localisation, the path integral localises onto configurations where the vectormultiplet scalar is non-zero and the gauge group is broken to a maximal torus. This expresses the partition function as a contour integral of special functions, for example, as in the first supersymmetric localisation computations on S 3 [1][2][3].…”

Section: A Quick Summarymentioning

confidence: 99%

“…6.1 U (1) 1 2 + 1 Chiral First consider k = 1 2 . In this case k eff (σ) = 1 2 (1 + sign(σ)) and therefore k + eff = 1 and k − eff = 0.…”

Section: Examplesmentioning

confidence: 99%

The Twisted Index and Topological Saddles

Bullimore¹,

Ferrari²,

Kim³

et al. 2020

Preprint

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The twisted index of 3d N = 2 gauge theories on S 1 × Σ has an algebro-geometric interpretation as the Witten index of an effective supersymmetric quantum mechanics. In this paper, we consider the contributions to the supersymmetric quantum mechanics from topological saddle points in supersymmetric localization of abelian gauge theories. Topological saddles are configurations where the matter fields vanish and the gauge symmetry is unbroken, which exist for non-vanishing effective Chern-Simons levels. We compute the contributions to the twisted index from both topological and vortex-like saddles points and show that their combination recovers the Jeffrey-Kirwan residue prescription for the twisted index and its wall-crossing.

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“…It was then desirable to reproduce the N 3 2 behavior of the degrees of freedom and figure out the corrections from the worldvolume theory Soon after, the partition function Z k (N) on S 3 was computed. By applying the localization technique for supersymmetric theories [5], the partition function, originally defined by the infinite-dimensional path integral, reduces to a finite-dimensional multiple integral, called the ABJM matrix model [6]. The 't Hooft large N expansion of the matrix model was studied and the degrees of freedom N 3 2 were reproduced [7] from the free energy log Z k (N) ≃ C − 1 2 N 3 2 with C = 2/(π 2 k).…”

Section: Introductionmentioning

confidence: 99%

Spectral Theories and Topological Strings on del Pezzo Geometries

Moriyama

2020

Preprint

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Motivated by understanding M2-branes, we propose to reformulate partition functions of M2-branes by quantum curves. Especially, we focus on the backgrounds of del Pezzo geometries, which enjoy Weyl group symmetries of exceptional algebras. We construct quantum curves explicitly and turn to the analysis of classical phase space areas and quantum mirror maps. We find that the group structure helps in clarifying previous subtleties, such as the shift of the chemical potential in the area and the identification of the overall factor of the spectral operator in the mirror map. We list the multiplicities characterizing the quantum mirror maps and find that the decoupling relation known for the BPS indices works for the mirror maps. As a result, with the group structure we can present explicitly the statement for the correspondence between spectral theories and topological strings on del Pezzo geometries.

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Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter

Cited by 351 publications

References 0 publications

Summing up all genus free energy of ABJM matrix model

Summing up all genus free energy of ABJM matrix model

The Twisted Index and Topological Saddles

Spectral Theories and Topological Strings on del Pezzo Geometries

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