Cardy Limits of 6d Superconformal Theories

Abstract

We explore the supersymmetric partition functions of 6d SCFTs on ${\mathbb{R}}^4\times T^2$ with non-vanishing charges for compatible global symmetries. We utilize the elliptic genera for self-dual strings and compute the free energy of 6d SCFTs in the Cardy limit. For a 6d (2,0) theory on $N$ M5-brane, we obtain the free energy proportional to $N^3$. We find that the origin of $N^3$ comes from the condensation of the self-dual strings, whose total number is proportional to $\frac{N^3-N}{6}$. We further extend our analysis to the general E-string theory and obtain its Cardy free energy.

38 pages, 8 figures

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• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• The Refined Topological Vertex
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• Anomaly polynomial of general 6d SCFTs
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Defects and Quantum Seiberg-Witten Geometry
• 6d, N=(1,0) Coulomb Branch Anomaly Matching
• On the Elliptic Genus of Three E-strings and Heterotic Strings

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