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ABJM theory as a Fermi gas

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Published in Journal of Statistical Mechanics: Theory and Experiment. 2012, vol. 2012
Abstract The partition function on the three-sphere of many supersymmetric Chern-Simons-matter 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 non-trivial, 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.
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arXiv: 1110.4066
Note 52 pages, 11 figures. v3: references, corrections and clarifications added, plus a footnote on the relation to the recent work by Hanada et al
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Other version: http://arxiv.org/abs/1110.4066
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MARINO BEIRAS, Marcos, PUTROV, Pavel. ABJM theory as a Fermi gas. In: Journal of Statistical Mechanics: Theory and Experiment, 2012, vol. 2012. https://archive-ouverte.unige.ch/unige:31058

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Deposited on : 2013-11-13

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