General instanton counting and 5d SCFT

Abstract

Instanton partition functions of 5d N=1 gauge theories are Witten indices for the ADHM gauged quantum mechanics with (0,4) SUSY. We derive the integral contour prescriptions for these indices using the Jeffrey-Kirwan method, for gauge theories with hypermultiplets in various representations. The results can be used to study various 4d/5d/6d QFTs. In this paper, we study 5d SCFTs which are at the UV fixed points of 5d SYM theories. In particular, we focus on the Sp(N) theories with N_f \leq 7 fundamental and 1 antisymmetric hypermultiplets, living on the D4-D8-O8 systems. Their superconformal indices calculated from instantons all show E_{N_f+1} symmetry enhancements. We also discuss some aspects of the 6d SCFTs living on the M5-M9 system. It is crucial to understand the UV incompleteness of the 5d SYM, coming from small instantons in our problem. We explain in our examples how to fix them. As an aside, we derive the index for general gauged quantum mechanics with (0,2) SUSY.

67 pages, 9 figures; v3: minor changes, published version

References in corpus (5)

• 5-dim Superconformal Index with Enhanced En Global Symmetry
• Witten Index and Wall Crossing
• Seiberg-Witten Theory and Random Partitions
• Superconformal Partition Functions and Non-perturbative Topological Strings
• An Index Formula for Supersymmetric Quantum Mechanics

Cited by in corpus (8)

• Witten Index and Wall Crossing
• Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories
• Duality and enhancement of symmetry in 5d gauge theories
• An Index Formula for Supersymmetric Quantum Mechanics
• On the Jeffrey-Kirwan residue of BCD-instantons
• Counting Trees in Supersymmetric Quantum Mechanics
• Asymptotics of Ground State Degeneracies in Quiver Quantum Mechanics
• Mutation, Witten Index, and Quiver Invariant