ABJM theory as a Fermi gas

By Marcos Mariño, Pavel Putrov. 2011

391 citations recorded by the source corpus.

The partition function on the 3-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 N3/2 behavior for ABJM theory and 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 D0- and D2-brane instantons in the AdS background.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fabf87c5af6587d6fe64f58b6f2d75769b2e4631

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Citations in the corpus

Instanton effects in ABJM theory from Fermi gas approach (2012, methodology): “One approach is to consider the ‘WKB’ (small k) expansions of the prefactors as in [9].”
Instanton bound states in ABJM theory (2013, methodology): “The perturbative part was computed in [9] and is given by”
Topological Strings from Quantum Mechanics (2014, methodology): “As first noted in [5], the study of this limit for the operators appearing in Chern–Simons–matter theories leads to many insights on their behavior, see for example [44, 45].”
Fivebranes and 3-manifold homology (2016, background): “In the case M3 = L(2, 1) the explicit form of such transform was found in [104, 105]”
The gravity dual of supersymmetric gauge theories on a squashed three-sphere (2011, methodology): “(7)Very recently we note that a completely different method has been found for computing this M-theory limit [41].”
Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant (2012, methodology): “12) by Fermi gas approach [35] for small k and with the constant map contribution for all k.”
A one-loop test of quantum supergravity (2012, methodology): “1) is independent of N, but it is a non-trivial function of ka and Nfa (see [4, 9] for explicit results on this coefficient in ABJM theory).”
Exact results on the ABJM Fermi gas (2012, methodology): “In [15, 17], it was shown that the ABJM partition function is written in terms of the Airy function if one neglects the instanton corrections.”