CFT in AdS and boundary RG flows

Abstract

Using the fact that flat space with a boundary is related by a Weyl transformation to anti-de Sitter (AdS) space, one may study observables in boundary conformal field theory (BCFT) by placing a CFT in AdS. In addition to correlation functions of local operators, a quantity of interest is the free energy of the CFT computed on the AdS space with hyperbolic ball metric, i.e. with a spherical boundary. It is natural to expect that the AdS free energy can be used to define a quantity that decreases under boundary renormalization group flows. We test this idea by discussing in detail the case of the large N critical O(N) model in general dimension d, as well as its perturbative descriptions in the epsilon-expansion. Using the AdS approach, we recover the various known boundary critical behaviors of the model, and we compute the free energy for each boundary fixed point, finding results which are consistent with the conjectured F-theorem in a continuous range of dimensions. Finally, we also use the AdS setup to compute correlation functions and extract some of the BCFT data. In particular, we show that using the bulk equations of motion, in conjunction with crossing symmetry, gives an efficient way to constrain bulk two-point functions and extract anomalous dimensions of boundary operators.

Holographic and localization calculations of boundary F for $$ \mathcal{N} $$ = 4 SUSY Yang-Mills theory

“…This quantity has also been conjectured to satisfy an RG monotonicity theorem in various dimensions [11,[16][17][18][19] (see [39][40][41] for proposed holographic g-functions); this has been proven in dimensions d = 2 and d = 3, with the results referred to as the g-theorem [8,9,20] and the b-theorem [21,22]. 7 In this paper, we will be specifically concerned with the case d = 4, where we have…”

“…2 BoundaryF may be defined from the partition function of the BCFT on a hemisphere, or from the vacuum entanglement entropy of a half-ball centered on the boundary. It is conjectured to decrease under boundary RG-flows (where a UV BCFT is perturbed by a relevant boundary operator) [11,[16][17][18][19]; this has been proven as the g-theorem in two dimensions [8,9,20] and the b-theorem in three dimensions [21,22], but remains a conjecture (the boundary F theorem) for four-dimensional BCFTs.…”

Defect extremal surface as the holographic counterpart of Island formula

“…Now we consider an interval [y 1 , 0] on the brane and calculate the entanglement entropy for the ground state of the brane CFT. Notice that CFT on AdS 2 can be mapped to a BCFT in flat space via a Weyl transformation [5,74]. One can read off the Weyl factor from the induced metric on the brane, ds 2 brane = Ω −2 (y)ds 2 flat , i.e.…”

Superconformal boundaries in 4 − ϵ dimensions

“…It was originally observed in [1] that the crossing equation for boundary CFTs can be used to extract information about the Wilson-Fischer fixed point in the epsilon expansion. In particular, they bootstrapped the one-loop correlators at order O( ), and the analysis was generalized to O( 2 ) using different techniques in later works [3,4,48]. In this section we apply the same ideas to our supersymmetric two-point functions, and we obtain the full correlation functions at order O( ).…”