Partial reduction and cosmology at defect brane

A bstract 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 2 d 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 4 d massless graviton on AdS 4 brane in partial reduction. We also propose a partial reduction for a 4 d FRW cosmology at defect brane and obtain the Newton constant by computing boundary entropy.