Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-11-30
JHEP 1001:090,2010
Physics
High Energy Physics
High Energy Physics - Theory
15 pages
Scientific paper
10.1007/JHEP01(2010)090
We consider ADE-type (2, 0) theory on a family of flat six-tori endowed with flat Sp(4) connections coupled to the R-symmetry. Our main objects of interest are the components of the `partition vector' of the theory. These constitute an element of a certain finite dimensional vector space, carrying an irreducible representation of a discrete Heisenberg group related to the 't Hooft fluxes of the theory. Covariance under the SL_6(Z) mapping class group of a six-torus amounts to a certain automorphic transformation law for the partition vector, which we derive. Because of the absence of a Lagrangian formulation of (2, 0) theory, this transformation property is not manifest, and gives useful non-trivial constraints on the partition vector. As an application, we derive a shifted quantization law for the spatial momentum of (2, 0) theory on a space-time of the form R x T5. This quantization law is in agreement with an earlier result based on the relationship between (2, 0) theory and maximally supersymmetric Yang-Mills theory together with certain geometric facts about gauge bundles.
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