Z. Naturforsch. 68a, 178 – 209
Aharony–Bergman–Jafferis–Maldacena Wilson Loops in the Fermi Gas Approach
1 Bethe Center for Theoretical Physics, Physikalisches Institut der Universität Bonn, Nussallee 12, D-53315 Bonn, Germany
2 Département de Physique Théorique et Section de Mathématiques, Université de Genève, Genève, CH-1211 Switzerland
Received November 29, 2012 / published online February 15, 2013
The matrix model of the Aharony–Bergman–Jafferis–Maldacena 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 Wentzel–Kramer–Brillouin expansion. We present explicit results for the vevs of 1/6 and the 1/2 Bogomolnyi–Prasad–Sommerfield 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.
Key words: Sring Gauge Theory, Duality, Strongly Coupled Systems.