Holographic entropy and Calabi’s diastasis

Abstract

The entanglement entropy for interfaces and junctions of two-dimensional CFTs is evaluated on holographically dual half-BPS solutions to six-dimensional Type 4b supergravity with m anti-symmetric tensor supermultiplets. It is shown that the moduli space for an N-junction solution projects to N points in the Kaehler manifold SO(2,m)/( SO(2) x SO(m)). For N=2 the interface entropy is expressed in terms of the central charge and Calabi's diastasis function on SO(2,m)/(SO(2) x SO(m)), thereby lending support from holography to a proposal of Bachas, Brunner, Douglas, and Rastelli. For N=3, the entanglement entropy for a 3-junction decomposes into a sum of diastasis functions between pairs, weighed by combinations of the three central charges, provided the flux charges are all parallel to one another or, more generally, provided the space of flux charges is orthogonal to the space of unattracted scalars. Under similar assumptions for N>3, the entanglement entropy for the N-junction solves a variational problem whose data consist of the N central charges, and the diastasis function evaluated between pairs of N asymptotic AdS_3 x S^3 regions.