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Zero-energy bound states of N=4 SYM on T^3: S-duality and the mapping class group

Måns Henningson (Institutionen för fundamental fysik) ; Niclas Wyllard (Institutionen för fundamental fysik)
Journal of High Energy Physics (1126-6708). Vol. 0804 (2008), p. 066.
[Artikel, refereegranskad vetenskaplig]

We continue our studies of the low-energy spectrum of N = 4 super-Yang-Mills theory on a spatial three-torus. In two previous papers, we computed the spectrum of normalizable zero-energy states for all choices of gauge group and all values of the electric and magnetic 't Hooft fluxes, and checked its invariance under the SL2(Z) S-duality group. In this paper, we refine the analysis by also decomposing the space of bound states into irreducible unitary representations of the SL3(Z) mapping class group of the three-torus. We perform a detailed study of the S-dual pairs of theories with gauge groups Spin(2n+1) and Sp(2n). The predictions of S-duality (which commutes with the mapping class group) are fulfilled as expected, but the proof requires some surprisingly intricate combinatorial infinite product identities.

Denna post skapades 2008-12-15. Senast ändrad 2014-11-10.
CPL Pubid: 81401


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