Zero-energy bound states of N=4 SYM on T^3: S-duality and the mapping class group
Artikel i vetenskaplig tidskrift, 2008

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.


Måns Henningson

Chalmers, Teknisk fysik, Elementarpartikelfysik

Niclas Wyllard

Chalmers, Fundamental fysik

Journal of High Energy Physics

1126-6708 (ISSN) 1029-8479 (eISSN)

Vol. 0804 066-


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