Low-energy spectrum of N = 4 super-Yang-Mills on T^3: flat connections, bound states at threshold, and S-duality

Details Low-energy spectrum of N = 4 super-Yang-Mills on T^3: flat connections, bound states at threshold, and S-duality Low-energy spectrum of N = 4 super-Yang-Mills on T^3: flat connections, bound states at threshold, and S-duality

2007-03-19

arxiv.org/abs/hep-th/0703172v2

JHEP 0706:001,2007

Physics

High Energy Physics

High Energy Physics - Theory

28 pages. v2:reference added

Scientific paper

10.1088/1126-6708/2007/06/001

We study (3+1)-dimensional N=4 supersymmetric Yang-Mills theory on a spatial three-torus. The low energy spectrum consists of a number of continua of states of arbitrarily low energies. Although the theory has no mass-gap, it appears that the dimensions and discrete abelian magnetic and electric 't Hooft fluxes of the continua are computable in a semi-classical approximation. The wave-functions of the low-energy states are supported on submanifolds of the moduli space of flat connections, at which various subgroups of the gauge group are left unbroken. The field theory degrees of freedom transverse to such a submanifold are approximated by supersymmetric matrix quantum mechanics with 16 supercharges, based on the semi-simple part of this unbroken group. Conjectures about the number of normalizable bound states at threshold in the latter theory play a crucial role in our analysis. In this way, we compute the low-energy spectra in the cases where the simply connected cover of the gauge group is given by SU(n), Spin(2n+1) or Sp(2n). We then show that the constraints of S-duality are obeyed for unique values of the number of bound states in the matrix quantum mechanics. In the cases based on Spin(2n+1) and Sp(2n), the proof involves surprisingly subtle combinatorial identities, which hint at a rich underlying structure.

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