ABJM theory as a Fermi gas
Oct, 2011Citations per year
Abstract: (arXiv)
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.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
- expansion: semiclassical
- expansion: strong coupling
- D-brane: instanton
- sphere: 3
- ABJM model
- Fermi gas
- partition function
- matrix model
- WKB approximation
- M-theory
References(60)
Figures(13)