Superconformal indices of $\mathcal{N}=4$ SYM field theories

Abstract

Superconformal indices (SCIs) of 4d $\mathcal{N}=4$ SYM theories with simple gauge groups are described in terms of elliptic hypergeometric integrals. For $F_4,E_6,E_7,E_8$ gauge groups this yields first examples of integrals of such type. S-duality transformation for G_2 and F_4 SCIs is equivalent to a change of integration variables. Equality of SCIs for SP(2N) and SO(2N+1) group theories is proved in several important special cases. Reduction of SCIs to partition functions of 3d $\mathcal{N}=2$ SYM theories with one matter field in the adjoint representation is investigated, corresponding 3d dual partners are found, and some new related hyperbolic beta integrals are conjectured.

19 pages; v. 2: a substantially improved version; v. 3: the paper was shortened by the demand of a Referee. New results on the reduction of 4d indices to 3d partition functions are added. Version to appear in Lett. Math. Phys

References in corpus (21)

• SUSY Gauge Theories on Squashed Three-Spheres
• Notes on SUSY Gauge Theories on Three-Sphere
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• S-duality in N=2 supersymmetric gauge theories
• Exactly Marginal Deformations and Global Symmetries
• From 4d superconformal indices to 3d partition functions
• Essays on the theory of elliptic hypergeometric functions
• The Superconformal Index of the E_6 SCFT
• Six-dimensional D_N theory and four-dimensional SO-USp quivers
• Superconformal indices for N=1 theories with multiple duals
• Calculating the Superconformal Index and Seiberg Duality
• Counting BPS operators in N=4 SYM
• Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
• N=4 Superconformal Characters and Partition Functions
• F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-Matter theories
• On S-duality for Non-Simply-Laced Gauge Groups
• Supersymmetric dualities beyond the conformal window
• On Conformal Deformations II
• Finite N Index and Angular Momentum Bound from Gravity
• Conformal Invariance = Finiteness and Beta Deformed N=4 SYM Theory
• Elliptic hypergeometric terms

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• Cardy-like asymptotics of the 4d $\mathcal{N}=4$ index and AdS${}_5$ blackholes
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• Asymptotic growth of the 4d $\mathcal{N}=4$ index and partially deconfined phases
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• On the ISS model of dynamical SUSY breaking
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• New N=1 dualities from orientifold transitions - Part II: String Theory
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• Elliptic beta integrals and solvable models of statistical mechanics
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• 3d $\mathcal{N}=2$ SO/USp adjoint SQCD: s-confinement and exact identites
• High-temperature asymptotics of the 4d superconformal index
• S-duality in the Cardy-like limit of the superconformal index
• Constraints on the R-charges of Free Bound States from the Römelsberger Index
• Strongly coupled phases of $\mathcal{N}=1$ S-duality