Supersymmetric Casimir Energy and the Anomaly Polynomial

Abstract

We conjecture that for superconformal field theories in even dimensions, the supersymmetric Casimir energy on a space with topology $S^1\times S^{D-1}$ is equal to an equivariant integral of the anomaly polynomial. The equivariant integration is defined with respect to the Cartan subalgebra of the global symmetry algebra that commutes with a given supercharge. We test our proposal extensively by computing the supersymmetric Casimir energy for large classes of superconformal field theories, with and without known Lagrangian descriptions, in two, four and six dimensions.

59 pages, 1 figure, v2: minor improvements, ref added

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• The Weyl Anomaly from the 6D Superconformal Index
• From Weyl Anomaly to Defect Supersymmetric Rényi Entropy and Casimir Energy
• Aspects of 4d supersymmetric dynamics and geometry