Multimatrix models and tri-Sasaki Einstein spaces

By Christopher P. Herzog, I. Klebanov, Silviu S. Pufu, Tiberiu Teşileanu. 2010

351 citations recorded by the source corpus.

Localization methods reduce the path integrals in N{>=}2 supersymmetric Chern-Simons gauge theories on S{sup 3} to multimatrix integrals. A recent evaluation of such a two-matrix integral for the N=6 superconformal U(N)xU(N) Aharony-Bergman-Jafferis-Maldacena theory produced detailed agreement with the AdS/CFT correspondence, explaining, in particular, the N{sup 3/2} scaling of the free energy. We study a class of p-matrix integrals describing N=3 superconformal U(N){sup p} Chern-Simons gauge theories. We present a simple method that allows us to evaluate the eigenvalue densities and the free energies in the large N limit keeping the Chern-Simons levels k{sub i} fixed. The dual M-theory backgrounds are AdS{sub 4}xY, where Y are seven-dimensional tri-Sasaki Einstein spaces specified by the k{sub i}. The gravitational free energy scales inversely with the square root of the volume of Y. We find a general formula for the p-matrix free energies that agrees with the available results for volumes of the tri-Sasaki Einstein spaces Y, thus providing a thorough test of the corresponding AdS{sub 4}/CFT{sub 3} dualities. This formula is consistent with the Seiberg duality conjectured for Chern-Simons gauge theories.

Subfields: Applied Mathematics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/18e980e55912e9ae2e68f10f8baf535942216c9e

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Citations in the corpus

Non-perturbative effects and the refined topological string (2013, methodology): “This was first done in [7], where the leading, large N limit was studied.”
Supersymmetry on curved spaces and holography (2012, background): “The statement about the N scaling can actually be made precise at the level of coefficients, also for theories with less supersymmetry [147, 148],”
A universal counting of black hole microstates in AdS4 (2017, background): “13) and the well-known expression for the holographic free energy on S(3) [47, 62]”
Rigid supersymmetric theories in curved superspace (2011, background): “Even though we do not discuss it here in detail, it is clear that the same issue with lack of reflection positivity applies to non-conformal N = 2 theories on S(4) [1-3] and on S(3) [4-20].”
Exact results on the ABJM Fermi gas (2012, methodology): “The study of the ABJM matrix model in the large N , finite k regime was initiated by [26] and further studied in [17] from the Fermi gas approach.”
Black hole microstates in AdS4 from supersymmetric localization (2015, methodology): “The dependence on u is exponentially suppressed and we observe an “absence of long-range forces” as in [20].”
Exact results for five-dimensional superconformal field theories with gravity duals (2012, methodology): “J H E P 0 5 ( 2 0 1 4 ) 0 3 2 such theories, it was possible to match the S3 free energy predicted from the gravity side with a field theory computation, and in particular to reproduce the N3/2 scaling using just field theory methods [15–19].”
ABJM theory as a Fermi gas (2011, methodology): “However, in the approach of [10] it is not obvious how to compute systematically 1/N corrections to the leading large N behavior, not to speak about exponentially small corrections in N .”
Reducing the 4d index to the S3 partition function (2011, background): “Remarkably, the exact partition function has also allowed for a direct field theory computation of N3/2 degrees of freedom of ABJM theory [11, 12].”
Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant (2012, methodology): “2 By using this matrix model, the free energy of the ABJM theory has been studied intensively [28, 29, 30, 31, 32, 33, 34, 35].”
Topological Strings from Quantum Mechanics (2014, methodology): “Second, our proposal can be regarded as a concrete M-theoretic version of the topological string, in the spirit of the M-theory expansion of Chern–Simons–matter theories [5, 23].”
Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories (2011, methodology): “Moreover, in [52], a very powerful method was introduced which makes possible to analyze the matrix models describing Chern–Simons–matter theories directly in the strong coupling limit, without the need to solve first for the resolvent.”
4d Index to 3d Index and 2d TQFT (2011, background): “Recent studies have uncovered powerful techniques (mostly based on localization) to extract exact results for 3d and 4d supersymmetric gauge theories, including the 4d N ≥ 1 superconformal index on S(1) × S(3) [1, 2], the 4d N ≥ 2 partition function on S(4) [3], the 3d N ≥ 2 partition function on S(”
F-theorem without supersymmetry (2011, methodology): “The solution of these matrix models in the large N limit [16, 20–24] produced perfect agreement with the AdS4/CFT3 correspondence, explaining in particular the N 3/2 scaling of the number of degrees of freedom expected on the gravity side of the duality [25].”