Spacetime Bananas with EOW Branes and Spins

TL;DR

This work extends the spacetime banana program in AdS$_3$/CFT$_2$ by introducing EOW branes and spinning subprocesses to compute holographic correlators of huge operators. The authors show that EOW branes enable a BCFT one-point function and that a refined micro-canonical action, rather than the naive GHY term alone, is essential for reproducing spinning two-point functions; they also reveal sign and coverage issues with FG-based Bańados/conical computations and propose resolutions via missing spacetime regions or brane insertions. The spinning banana construction yields a magnitude consistent with the expected tensor structure when supplemented by an imaginary twist term, providing a path toward the full spin-dependent two-point function. The work also discusses dS, JT gravity, and holographic local quench extensions, highlighting the universality and potential limitations of the spacetime banana approach across dimensions and geometries.

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.

Figures (8)

• Figure 1: The holographic dual of the one-point function is the region shown in yellow bounded by the stretched horizon, AdS boundary, and two EOW branes. The red line denotes the horizon and the dotted blue lines denote the EOW branes. Moreover, the two vertical green lines are used to project the intersection points of the EOW brane and regulator surface with the horizon, to the boundary at $Z=0$.
• Figure 2: The EOW brane can only enclose one of the two inserted operators. Here the dashed blue circles are the projection of the EOW branes on the boundary. With the special value $b_x r_{\operatorname{d} }=1$, the EOW brane becomes a plane that cuts the banana in half. In this case, the projection of the EOW brane on the boundary is shown by a vertical blue dashed line.
• Figure 3: We can use two EOW branes to enclose the horizon of the black hole. These branes are shown by blue and red dashed curves. Moreover, the yellow region is outside the horizon and enclosed by the two EOW branes. Here we calculate the bulk on-shell action $I_{\rm EH}$ inside this region.
• Figure 4: The two EOW branes form a tilted cone outside the cone corresponding to the stretched horizon.
• Figure 5: Under the GtP transformations, a spinning circle is mapped to a helix in the cone geometry. Here we set $r_0=1,a=\frac{1}{2}$.