Nonrenormalization theorem for $ \mathcal{N} $ = (4, 4) interface entropy

A bstract: We derive a formula for the half-BPS interface entropy between any pair of $$ \mathcal{N} $$ N = (4, 4) theories on the same conformal manifold. This generalizes the diastasis formula derived in [1] for $$ \mathcal{N} $$ N = (2, 2) theories, which is restricted to the conformal submanifolds generated by either chiral or twisted chiral multiples of $$ \mathcal{N} $$ N = (2, 2) supersymmetry. To derive the $$ \mathcal{N} $$ N = (4, 4) formula, we use the fact that the conformal manifold of $$ \mathcal{N} $$ N = (4, 4) theories is symmetric and quaternionic-Kähler and that its isotropy group contains the SU(2) ⊗ SU(2) external automorphism of the $$ \mathcal{N} $$ N = (4, 4) superconformal algebra. As an application of the formula, we prove a supersymmetric non-renormalization theorem, which explains the observation in [2] that the interface entropy for half-BPS Janus solutions in type IIB supergravity on AdS ₃ × S ³ × T ⁴ coincides with the corresponding quantity in their free conformal field limits.