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

TL;DR

This paper derives a non-renormalization formula for interface entropy in ${ m N}=(4,4)$ theories, extending previous results for ${ m N}=(2,2)$, and proves it explains the invariance of entropy in certain supergravity solutions.

Contribution

It provides the first explicit formula for ${ m N}=(4,4)$ interface entropy and demonstrates its non-renormalization property, generalizing earlier ${ m N}=(2,2)$ results.

Findings

Derived a formula for ${ m N}=(4,4)$ interface entropy.

Proved a non-renormalization theorem for the entropy.

Showed the entropy matches free theory calculations in supergravity solutions.

Abstract

We derive a formula for the half-BPS interface entropy between any pair of ${\cal N}=(4,4)$ theories on the same conformal manifold. This generalizes the diastasis formula derived in arXiv:1311.2202 for ${\cal N}=(2,2)$ theories, which is restricted to the conformal submanifolds generated by either chiral or twisted chiral multiples of ${\cal N}=(2,2)$ supersymmetry. To derive the ${\cal N}=(4,4)$ formula, we use the fact that the conformal manifold of ${\cal N}=(4,4)$ theories is symmetric and quaternionic-K\"ahler and that its isotropy group contains the $SU(2) \otimes SU(2)$ external automorphism of the ${\cal N}=(4,4)$ 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 ${\it AdS}_3 \times S^3 \times T^4$ coincides with the corresponding quantity in their free conformal field limits.