Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories

Santamaría, Ricardo Couso; Mariño, Marcos; Putrov, Pavel

doi:10.1007/jhep10(2011)139

Cited by 32 publications

(16 citation statements)

References 62 publications

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“…Thus there is hope that the present matrix model will provide the famous N 3 dependence [21] of the free energy in the large N-limit. For the matrix models arising from localization of 3D gauge theories [8,10,11,12,13] the famous N 3/2 dependence of the free energy has been successfully demonstrated in different models, see for example [22,23,24,25,26,27,13]. For a nice review, see [28].…”

Section: Y Mmentioning

confidence: 99%

The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere

Kallen

Qiu

Zabzine

2012

J. High Energ. Phys.

154

237

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Based on the construction by Hosomichi, Seong and Terashima we consider N = 1 supersymmetric 5D Yang-Mills theory with matter on a five-sphere with radius r. This theory can be thought of as a deformation of the theory in flat space with deformation parameter r and this deformation preserves 8 supercharges. We calculate the full perturbative partition function as a function of r/g 2 Y M , where g Y M is the Yang-Mills coupling, and the answer is given in terms of a matrix model. We perform the calculation using localization techniques. We also argue that in the large N -limit of this deformed 5D Yang-Mills theory this matrix model provides the leading contribution to the partition function and the rest is exponentially suppressed.

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Section: Y Mmentioning

confidence: 99%

The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere

Kallen

Qiu

Zabzine

2012

J. High Energ. Phys.

154

237

View full text Add to dashboard Cite

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“…earlier works [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]. Especially it is worthwhile to mention that, according to [15] the expression of the coefficient C was given a geometrical interpretation as the classical volume inside the Fermi surface.…”

Section: Jhep11(2014)164mentioning

confidence: 99%

Partition functions of superconformal Chern-Simons theories from Fermi gas approach

Moriyama

Nosaka

2014

J. High Energ. Phys.

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Abstract:We study the partition function of three-dimensional N = 4 superconformal Chern-Simons theories of the circular quiver type, which are natural generalizations of the ABJM theory, the worldvolume theory of M2-branes. In the ABJM case, it was known that the perturbative part of the partition function sums up to the Airy function as Z(N ) = e A C −1/3 Ai[C −1/3 (N − B)] with coefficients C, B and A and that for the non-perturbative part the divergences coming from the coefficients of worldsheet instantons and membrane instantons cancel among themselves. We find that many of the interesting properties in the ABJM theory are extended to the general superconformal Chern-Simons theories. Especially, we find an explicit expression of B for general N = 4 theories, a conjectural form of A for a special class of theories, and cancellation in the non-perturbative coefficients for the simplest theory next to the ABJM theory.

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“…This result raises an interesting possibility. The N 3/2 behavior of the free energy characterizes a large class of N = 3 [10,11] and N = 2 [12,13,14,15] Chern-Simons-matter theories. On the other hand, the result (1.1) says that, for ABJM theory, this behavior is just the leading term in the logarithm of the Airy function.…”

Section: Introductionmentioning

confidence: 99%

ABJM theory as a Fermi gas

Mariño¹,

Putrov²

2012

J. Stat. Mech.

Self Cite

284

874

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The partition function on the three-sphere of many supersymmetric Chern-Simonsmatter theories reduces, by localization, to a matrix model. We develop a new method to study these models in the M-theory limit, but at all orders in the 1/N expansion. The method is based on reformulating the matrix model as the partition function of an ideal Fermi gas with a nontrivial, one-particle quantum Hamiltonian. This new approach leads to a completely elementary derivation of the N 3/2 behavior for ABJM theory and N = 3 quiver Chern-Simons-matter theories. In addition, the full series of 1/N corrections to the original matrix integral can be simply determined by a next-to-leading calculation in the WKB or semiclassical expansion of the quantum gas, and we show that, for several quiver Chern-Simons-matter theories, it is given by an Airy function. This generalizes a recent result of Fuji, Hirano and Moriyama for ABJM theory. It turns out that the semiclassical expansion of the Fermi gas corresponds to a strong coupling expansion in type IIA theory, and it is dual to the genus expansion. This allows us to calculate explicitly non-perturbative effects due to D2-brane instantons in the AdS background. arXiv:1110.4066v3 [hep-th]

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Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories

Cited by 32 publications

References 62 publications

The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere

The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere

Partition functions of superconformal Chern-Simons theories from Fermi gas approach

ABJM theory as a Fermi gas

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