Automorphic properties of (2, 0) theory on T6

Understand

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.