Modular properties of full 5D SYM partition function

Abstract

We study properties of the full partition function for the $U(1)$ 5D $\mathcal{N}=2^{\ast }$ 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 $G_2^C$ associated with a certain moment map cone $C$. The answer exhibits a curious $SL(4,\mathbb{Z})$ 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.

32 pages, refs and comments added, example added

References in corpus (6)

• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills
• On D=5 super Yang-Mills theory and (2,0) theory
• Defects and Quantum Seiberg-Witten Geometry
• The Superconformal Index of the (2,0) Theory with Defects
• Gluing Nekrasov partition functions

Cited by in corpus (4)

• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• Supersymmetric Rényi Entropy and Defect Operators
• 7D supersymmetric Yang-Mills on curved manifolds
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs