Holographic Correlators of Boundary/Crosscap CFTs in Two Dimensions

TL;DR

This paper studies holographic correlators in 2D BCFT and XCFT using AdS/CFT, deriving recurrence relations, analyzing brane tension effects, and exploring correlators on projective geometries and finite cutoffs.

Contribution

It introduces new methods for computing holographic correlators in BCFT and XCFT, including recurrence relations and tension effects, expanding understanding of holographic duals in two dimensions.

Findings

Derived recurrence relations for two- and three-point correlators.

Analyzed the effects of brane tension on correlator structures.

Computed correlators on projective geometries like $ ext{RP}^2$.

Abstract

This work explores holographic correlators within the frameworks of two-dimensional Boundary Conformal Field Theory (BCFT) and Crosscap Conformal Field Theory (XCFT). Utilizing the AdS/CFT correspondence, we compute stress tensor correlators in BCFT, considering both tensionless and tensionful end-of-the-world (EOW) brane scenarios. We derive recurrence relations for two-point and three-point correlators and examine the impact of non-zero brane tension on correlators. Extending these results, we investigate the holographic duals of XCFTs, presenting explicit scalar and stress tensor correlator computations on projective geometries such as $\mathbb{RP}^2$. Additionally, we analyze stress tensor correlators at a finite cutoff, uncovering deformations to one-point and two-point functions induced by the cutoff. Our findings provide novel insights into the holographic structures of BCFT and XCFT while laying the groundwork for future research into higher-dimensional extensions.