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ABJM Wilson Loops in the Fermi Gas Approach

Klemm, Albrecht
Schiereck, Marc
Soroush, Masoud
Published in Zeitschrift für Naturforschung. A. 2013, vol. 68a, p. 178-209
Abstract The matrix model of the ABJM theory can be formulated in terms of an ideal Fermi gas with a non-trivial one-particle Hamiltonian. We show that, in this formalism, vacuum expectation values (vevs) of Wilson loops correspond to averages of operators in the statistical-mechanical problem. This makes it possible to calculate these vevs at all orders in 1/N, up to exponentially small corrections, and for arbitrary Chern–Simons coupling, by using the WKB expansion. We present explicit results for the vevs of 1/6 and the 1/2 BPS Wilson loops, at any winding number, in terms of Airy functions. Our expressions are shown to reproduce the low genus results obtained previously in the 't Hooft expansion.
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Other version: http://www.znaturforsch.com/aa/v68a/0118-12.htm
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KLEMM, Albrecht et al. ABJM Wilson Loops in the Fermi Gas Approach. In: Zeitschrift für Naturforschung. A, 2013, vol. 68a, p. 178-209. https://archive-ouverte.unige.ch/unige:34938

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Deposited on : 2014-03-24

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