ABJM Wilson loops in the Fermi gas approach
High Energy Physics - Theory
2015-03-20 v2
Abstract
The matrix model of ABJM theory can be formulated in terms of a Fermi gas in an external potential. We show that, in this formalism, 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.
Cite
@article{arxiv.1207.0611,
title = {ABJM Wilson loops in the Fermi gas approach},
author = {Albrecht Klemm and Marcos Marino and Marc Schiereck and Masoud Soroush},
journal= {arXiv preprint arXiv:1207.0611},
year = {2015}
}
Comments
48 pages, 2 figures, expansion (2.110) and typos corrected, slight improvements of the presentation