Analytic bootstrap in 2D boundary conformal field theory: towards braneworld holography

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.

BCFT and Islands in two dimensions

“…The AdS/BCFT has been applied to many problems. This includes the studied of renormalization group flow[63][64][65][66], applications to models in condensed matter physics or statistical mechanics[67][68][69][70][71][72][73][74][75], to eigenstate thermalization hypothesis[76,77] and to computational complexity[78][79][80][81]. Refer also to[53,[82][83][84][85][86][87][88] for string theory embeddings, to[89][90][91][92] for application to cosmological models and to[93,94] for higher codimension holography.…”

Holographic Local Operator Quenches in BCFTs

“…It is interesting to take the matter contribution as well [14]. The BCFT counterpart might be calculated by taking a certain limit such as the Regge limit [50,16], which is presumably related to α → 0 limit. Another intriguing problem is to explore the brane-world interpretation of our holographic local quench in a BCFT, which allows us to interpret it as a two-dimensional gravity coupled to a CFT and which relates our entanglement entropy computation to the island formula.…”

“…This distinction becomes crucial when we discuss the first law of entanglement. 16 ω is not the complex conjugate of ω but is defined from z.…”

“…the holographic entanglement entropy formula for AdS/BCFT in the presence of EOW branes [3,4] takes the identical form as the island formula [9,10,11,12,13] which computes the entanglement entropy in the presence of gravity. This correspondence can be regarded as an equivalence between a BCFT and a CFT coupled to gravity, as systematically studied recently in [14] (see also [15,16] for related studies from conformal field theoretic approaches). In this way, these ideas of EOW branes are deeply connected at the bottom and their further understandings are expected to be a key ingredient to fully understand quantum gravity.…”

Partial Reduction and Cosmology at Defect Brane

“…This will tell us the fine grained entropy of a de-Sitter cosmology. Last but not least, following our construction from partial reduction, using defect and boundary CFT techniques one can try to bootstrap [51,52] the evolutional cosmology, which will eventually open the door to simulating our observational cosmology on quantum computer.…”