Spacetime Bananas with EOW Branes and Spins

Abstract

In this work, we study and generalize the spacetime banana proposal for computing correlation functions of huge operators in the context of the AdS$_3$/CFT$_2$ correspondence. First, we introduce time-like and space-like EOW branes into the proposal and demonstrate that: 1) a holographic dual of the one-point function in a BCFT can be obtained and its modified on-shell action reproduces the expected BCFT result; and 2) the GHY term on the stretched horizon can be replaced by the action of an EOW brane which wraps the horizon. Next, we discuss the two (one)-point function of huge spinning operators described by a rotating black hole in the bulk. We show that simply adding a GHY term on the stretched horizon is insufficient to reproduce the CFT results; instead, the appropriate modified action should be the micro-canonical action. Finally, we revisit the existing approaches for computing correlation functions using the gravity on-shell action of conical geometry or Ba$\tilde{\text{n}}$ados geometries. Surprisingly, we find that the on-shells actions of the Ba$\tilde{\text{n}}$ados geometries or the gravity solutions in the FG gauge yield unexpected incorrect results.