Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index

Abstract

We provide the geometrical meaning of the $\mathcal{N}=4$ superconformal index. With this interpretation, the $\mathcal{N}=4$ superconformal index can be realized as the partition function on a Scherk-Schwarz deformed background. We apply the localization method in TQFT to compute the deformed partition function since the deformed action can be written as a ${\delta }_{\epsilon }$-exact form. The critical points of the deformed action turn out to be the space of flat connections which are, in fact, zero modes of the gauge field. The one-loop evaluation over the space of flat connections reduces to the matrix integral by which the $\mathcal{N}=4$ superconformal index is expressed.

42+1 pages, 2 figures, JHEP style: v1.2.3 minor corrections, v4 major revision, conclusions essentially unchanged, v5 published version

References in corpus (16)

• 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
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• From 4d superconformal indices to 3d partition functions
• Seiberg-Witten Theory and Random Partitions
• Relation between the 4d superconformal index and the S^3 partition function
• Superconformal indices for N=1 theories with multiple duals
• Calculating the Superconformal Index and Seiberg Duality
• On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check
• Comments on 1/16 BPS Quantum States and Classical Configurations
• N=4 Superconformal Characters and Partition Functions
• N=4 SYM on R x S^3 and Theories with 16 Supercharges
• Index for Supergravity on AdS_5 \times T^{1,1} and Conifold Gauge Theory
• Supersymmetric dualities beyond the conformal window
• On R-symmetric Fixed Points and Superconformality

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• Line Operator Index on S1 $\times$ S3
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