Instantons on the 5-sphere and M5-branes

Abstract

We calculate the partition functions of supersymmetric gauge theories on S^5, which acquire non-perturbative contributions from instanton loops wrapping its Hopf fiber. The instantons on the CP^2 base equivariantly localize to 3 fixed points of SU(3) Cartans. Using our results, we study the index of the 6d (2,0) theory. We first study the partition functions of maximal SYM with AD(E) gauge groups, which agree with the gravity dual indices on AdS_7 in the large N limits. We also show that the most general partition function of the Abelian theory agrees with the index for a free 6d tensor supermultiplet. We explain possible ambiguities in our 5d approach, role of maximal SUSY, and the Wilson loops on S^5 dual to M2-brane Wilson surfaces in AdS_7.

60 pages, no figures

References in corpus (5)

• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• 5-dim Superconformal Index with Enhanced En Global Symmetry
• Supersymmetric Gauge Theories on the Five-Sphere
• Superconformal Partition Functions and Non-perturbative Topological Strings
• Vortices and 3 dimensional dualities

Cited by in corpus (12)

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• E + E $\to$ H
• Supersymmetric Rényi Entropy in Five Dimensions
• Holography of 3d-3d correspondence at Large N
• M5-branes and Wilson Surfaces in AdS${}_7$/CFT${}_6$ Correspondence
• On AGT-W Conjecture and q-Deformed W-Algebra
• 5d Higgs Branch Localization, Seiberg-Witten Equations and Contact Geometry
• Lattice Gerbe Theory
• Phases of planar 5-dimensional supersymmetric Chern-Simons theory
• Partition functions for equivariantly twisted $\mathcal{N}=2$ gauge theories on toric Kähler manifolds
• The ADHM-like Constructions for Instantons on CP^2 and Three Dimensional Gauge Theories