Partial reduction and cosmology at defect brane

Abstract Partial reduction is a Karch-Randall reduction for only part of the AdS region between finite tension brane and zero tension brane. This is interesting in AdS/BCFT where the AdS bulk contains a defect brane. We employ partial reduction for a AdS bulk with a brane evolving as a 2d Friedmann-Robertson-Walker (FRW) cosmology and demonstrate the equivalence between defect extremal surface and island formula for a large subregion fine grained entropy in boundary CFT. We then move to higher dimensions and demonstrate the existence of 4d massless graviton on AdS4 brane in partial reduction. We also propose a partial reduction for a 4d FRW cosmology at defect brane and obtain the Newton constant by computing boundary entropy.