The large N limit of quiver matrix models and Sasaki-Einstein manifolds

By D. Martelli, J. Sparks. 2011

140 citations recorded by the source corpus.

We study the matrix models that result from localization of the partition functions of N=2 Chern-Simons-matter theories on the three-sphere. A large class of such theories are conjectured to be holographically dual to M-theory on Sasaki-Einstein seven-manifolds. We study the M-theory limit (large N and fixed Chern-Simons levels) of these matrix models for various examples, and show that in this limit the free energy reproduces the expected AdS/CFT result of N^{3/2}/Vol(Y)^{1/2}, where Vol(Y) is the volume of the corresponding Sasaki-Einstein metric. More generally we conjecture a relation between the large N limit of the partition function, interpreted as a function of trial R-charges, and the volumes of Sasakian metrics on links of Calabi-Yau four-fold singularities. We verify this conjecture for a family of U(N)^2 Chern-Simons quivers based on M2 branes at hypersurface singularities, and for a U(N)^3 theory based on M2 branes at a toric singularity.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b5cfdca2632c9cd8f16ceea2d0f20a76e3a37dfc

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Citations in the corpus

The gravity dual of supersymmetric gauge theories on a squashed three-sphere (2011, methodology): “A key point, observed in [30], is that for an appropriate class of non-chiral Chern-Simons quiver theories, these long ranges forces automatically cancel.”
Supersymmetry on curved spaces and holography (2012, methodology): “With this procedure our candidate Fg is always polynomial in the R charges, contrary with the known examples computed in the literature [18, 138] and in chapter 10, where the free energy at large N is a rational function of the R charges of the fields and monopoles.”
Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories (2011, unknown): “tremize the anomaly a-coecient [50], and the result of [51] leads naturally to the conjecture [52]. The extremization property proved in [51] has been applied and tested in { 60 { various situations [70, 22, 52, 9], although the validity of the F-theorem is still conjectural and possible counterexam”
ABJM theory as a Fermi gas (2011, background): “TheN3/2 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.”
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].”
F-theorem without supersymmetry (2011, methodology): “Also, for large N theories with AdS4 × Y7 dual descriptions in M-theory, F -maximization is correctly mapped to the minimization of the volume of the Sasaki-Einstein spaces Y7 [19, 26].”
Reducing the 4d index to the S3 partition function (2011, background): “s also allowed for a direct ﬁeld theory computation of N3/2 degrees of freedom of ABJM theory [11, 12]. The S3 partition function of N = 2 theories is extremized by the exact superconformal Rsymmetry [13, 14, 15] so just like the a-maximization in 4d, the 3d partition function can be used to determi”
Relation between the 4d superconformal index and the S3 partition function (2011, methodology): “It is used to confirm dualities among 3d theories [4, 5, 6, 7] and predictions of AdS4/CFT3 [8, 9, 10, 11, 12].”
The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere (2012, methodology): “For the matrix models arising from localization of 3D gauge theories [8, 10–13] the famous N3/2 dependence of the free energy has been successfully demonstrated in different models, see for example [13, 21–26].”
Towards the F-theorem: $ \mathcal{N} = 2 $ field theories on the three-sphere (2011, result): “Note Added After the calculations presented here were completed, and as the paper was being finalized, we received two papers [59, 60] that partly overlap with our results.”
Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories (2012, methodology): “As was pointed out in [9,61], the F -maximization principle is closely related to the volume minimization procedure of [62,63].”