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

TL;DR

This work tackles universal properties of irrational BCFTs in 2D and their potential gravity duals within braneworld holography.It develops an analytic bootstrap based on fusion-matrix transformations to derive asymptotic formulas for boundary spectra and boundary/bulk OPE coefficients across diverse BCFT configurations.Key results include a Cardy-type density for boundary primaries, universal OPE asymptotics governed by fusion kernels, and light-cone bootstrap extensions that reveal ETH-like behavior in holographic BCFTs.The framework provides a bridge between BCFT data and braneworld gravity, offering analytic tools to probe the boundary sector that may encode gravitational dynamics on the brane.

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.

Figures (6)

• Figure 1: Triality through the AdS/CFT correspondence. The CFT drawn in the left is dual to the BCFT drawn in the right through the AdS/CFT correspondence. Moreover, the BCFT is dual to the quantum gravity shown at the bottom through the AdS/BCFT correspondence. There is also a relation between the left picture and the bottom picture through the braneworld holography Karch2001Randall1999Randall1999a.
• Figure 2: The definition of the boundary operator. The index $I$ labels a primary field with the conformal dimension $h_I$ and the indices $a,b$ denote its boundary conditions, where the boundary condition $a$ is changed to $b$ by the operator $\phi^{ab}_I$.
• Figure :
• Figure :
• Figure :