Nonrenormalization Theorem for $\mathcal{N}=(4,4)$ Interface Entropy

Abstract

We derive a formula for the half-BPS interface entropy between any pair of $\mathcal{N}=(4,4)$ theories on the same conformal manifold. This generalizes the diastasis formula derived in arXiv:1311.2202 for $\mathcal{N}=(2,2)$ theories, which is restricted to the conformal submanifolds generated by either chiral or twisted chiral multiples of $\mathcal{N}=(2,2)$ supersymmetry. To derive the $\mathcal{N}=(4,4)$ formula, we use the fact that the conformal manifold of $\mathcal{N}=(4,4)$ theories is symmetric and quaternionic-Kähler and that its isotropy group contains the $SU(2)\otimes SU(2)$ external automorphism of the $\mathcal{N}=(4,4)$ superconformal algebra. As an application of the formula, we prove a supersymmetric non-renormalization theorem, which explains the observation in arXiv:1005.4433 that the interface entropy for half-BPS Janus solutions in type IIB supergravity on ${AdS}_3\times S^3\times T^4$ coincides with the corresponding quantity in their free conformal field limits.