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**1 - 8**of**8**### Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach

, 2014

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### Article Reference M-theoretic matrix models

"... Some matrix models admit, on top of the usual ’t Hooft expansion, an M-theory-like expansion, i.e. an expansion at large N but where the rest of the parameters are fixed, instead of scaling with N. These models, which we call M-theoretic matrix models, appear in the localization of Chern-Simons-matt ..."

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Some matrix models admit, on top of the usual ’t Hooft expansion, an M-theory-like expansion, i.e. an expansion at large N but where the rest of the parameters are fixed, instead of scaling with N. These models, which we call M-theoretic matrix models, appear in the localization of Chern-Simons-matter theories, and also in two-dimensional statistical physics. Generically, their partition function receives non-perturbative corrections which are not captured by the ’t Hooft expansion. In this paper, we discuss general aspects of these type of matrix integrals and we analyze in detail two different examples. The first one is the matrix model computing the partition function of N = 4 $ $ \mathcal{N}=4 $ $ supersymmetric Yang-Mills theory in three dimensions with one adjoint hypermultiplet and N f fundamentals, which has a conjectured M-theory dual, and which we call the N f matrix model. The second one, which we call the polymer matrix model, computes form factors of the 2d Ising model and is related to the physics of 2d polymers. In both cases we determine their exact planar limit. In the N f matrix model, the planar free [...]

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, 2006

"... Abstract: We consider pure spinor strings that propagate in the background generated by a sequence of TsT transformations. We use the fact that U(1) isometry variables of TsT-transformed background are related to the isometry variables of the initial background in the universal way that is independe ..."

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Abstract: We consider pure spinor strings that propagate in the background generated by a sequence of TsT transformations. We use the fact that U(1) isometry variables of TsT-transformed background are related to the isometry variables of the initial background in the universal way that is independent of the details of the background. We will argue that after redefinitions of pure spinors and the fermionic variables we can construct pure spinor action with manifest U(1) isometry. This fact implies that the pure spinor string in TsT-transformed background is described by pure spinor string in the original background where world-volume modes are subject to twisted boundary conditions. We will argue that these twisted boundary conditions generally prevent to prove the quantum conformal invariance of the pure spinor string in AdS5 × S 5 background. We determine the conditions under which this quantum conformal invariance can be proved. We also determine the Lax pair for pure spinor strings in the TsT-transformed background.