Analytic Bootstrap in 2D Boundary Conformal Field Theory: Towards Braneworld Holography

TL;DR

This paper uses conformal bootstrap techniques to analyze irrational boundary conformal field theories, aiming to deepen understanding of their role in braneworld holography and quantum gravity dualities.

Contribution

It introduces the first bootstrap-based analysis of irrational BCFT boundary data relevant to braneworld holography, expanding the study beyond rational BCFTs.

Findings

Boundary primary spectrum characterized

Boundary OPE coefficients analyzed

Insights into bulk-boundary relations obtained

Abstract

Recently, boundary conformal field theories (BCFTs) have attracted much attention in the context of quantum gravity. This is because a BCFT can be dual to gravity coupled to a heat bath CFT, known as the island model. On this background, it would be interesting to explore the duality between the boundary and the braneworld. However, this seems to be a challenging problem. The reason is because although there has been much study of rational BCFTs, there has been comparatively little study of irrational BCFTs, and irrational BCFTs are expected to be the boundary duals of the braneworlds. For this reason, we explore properties of boundary ingredients: the boundary primary spectrum, the boundary-boundary-boundary OPE coefficients and the bulk-boundary OPE coefficients. For this purpose, the conformal bootstrap is extremely useful. This is the first step in providing an understanding of BCFTs in the context of braneworld holography by using the conformal bootstrap. The techniques developed in this paper may be useful for further investigation of irrational BCFTs.