Modular properties of full 5D SYM partition function

Abstract

We study properties of the full partition function for the U(1) 5D N = 2 * gauge theory with adjoint hypermultiplet of mass M . This theory is ultimately related to abelian 6D (2,0) theory. We construct the full non-perturbative partition function on toric Sasaki-Einstein manifolds by gluing flat copies of the Nekrasov partition function and we express the full partition function in terms of the generalized double elliptic gamma function G C 2 associated with a certain moment map cone C. The answer exhibits a curious SL(4, Z) modular property. Finally, we propose a set of rules to construct the partition function that resembles the calculation of 5d supersymmetric partition function with the insertion of defects of various co-dimensions.

7D supersymmetric Yang-Mills on curved manifolds

“…These vertices are where the total T 4 action degenerates to an S 1 action which is the Reeb orbit. This story is similar to what is happening in 5D, [43]. Now let us discuss S 7 as an SU(2)-fibration over S 4 .…”

q-Virasoro Modular Triple

“…More generally, one would expect that there exist other "modular multiple" constructions that should be associated to gauge theories on S 3 /Z k and their intersecting unions in other Sasaki-Einstein manifolds [32,35,62]. It would be interesting to study the modular properties [63][64][65] from this perspective.…”

Supersymmetric Rényi entropy and defect operators

“…If this is the case, a relationship similar to the one described here should hold for the partition functions on four-manifolds and five-manifolds of the type described in e.g. [65,66].…”