The O(N ) model with ϕ6 potential in ℝ2 × ℝ+

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.

“…We will restrict to the case of unitary theories, and so we will only consider solutions satisfying the boundary unitarity bound. The existence of these saddles was also noted in [4].…”

Section: Jhep11(2020)118mentioning

confidence: 68%

Section: Introductionmentioning

confidence: 64%

See 1 more Smart Citation

CFT in AdS and boundary RG flows

Giombi

Khanchandani

2020

“…Recently there have been a lot of research focused on higher dimensional (in dimensions greater than two) conformal field theories (CFT's) in the presence of a boundary (see e.g. [1][2][3][4]) or a defect (see e.g. [5][6][7][8]).…”

Section: Introductionmentioning

confidence: 99%

Fusion of conformal defects in four dimensions

Söderberg

2021

We consider two conformal defects close to each other in a free theory, and study what happens as the distance between them goes to zero. This limit is the same as zooming out, and the two defects have fused to another defect. As we zoom in we find a non-conformal effective action for the fused defect. Among other things this means that we cannot in general decompose the two-point correlator of two defects in terms of other conformal defects. We prove the fusion using the path integral formalism by treating the defects as sources for a scalar in the bulk.

“…This idea has been recently used to compute the one-loop twopoint function of the order parameter in the extraordinary phase transition of the O(N ) model [56,57]. One can also apply it to the O(N ) model in the large-N limit, see [58] for the three-dimensional case with a φ 6 potential.…”

Section: Using Susceptibilitymentioning

confidence: 99%

Superconformal boundaries in 4 − ϵ dimensions

Liendo

Vliet

2021

Boundaries in three-dimensional $$ \mathcal{N} $$ N = 2 superconformal theories may preserve one half of the original bulk supersymmetry. There are two possibilities which are characterized by the chirality of the leftover supercharges. Depending on the choice, the remaining 2d boundary algebra exhibits $$ \mathcal{N} $$ N = (0, 2) or $$ \mathcal{N} $$ N = (1) supersymmetry. In this work we focus on correlation functions of chiral fields for both types of supersymmetric boundaries. We study a host of correlators using superspace techniques and calculate superconformal blocks for two- and three-point functions. For $$ \mathcal{N} $$ N = (1) supersymmetry, some of our results can be analytically continued in the spacetime dimension while keeping the codimension fixed. This opens the door for a bootstrap analysis of the ϵ-expansion in supersymmetric BCFTs. Armed with our analytically-continued superblocks, we prove that in the free theory limit two-point functions of chiral (and antichiral) fields are unique. The first order correction, which already describes interactions, is universal up to two free parameters. As a check of our analysis, we study the Wess-Zumino model with a super-symmetric boundary using Feynman diagrams, and find perfect agreement between the perturbative and bootstrap results.