Kavli Affiliate: Hirosi Ooguri
| Summary:
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-Kähler 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.
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