Anomalous dimensions in the WF O(N) model with a monodromy line defect

107

191

We study the O(N ) and Gross-Neveu models at large N on AdS d+1 background.Thanks to the isometries of AdS, the observables in these theories are constrained by the SO(d, 2) conformal group even in the presence of mass deformations, as was discussed by Callan and Wilczek [1], and provide an interesting two-parameter family of quantities which interpolate between the S-matrices in flat space and the correlators in CFT with a boundary. For the actual computation, we judiciously use the spectral representation to resum loop diagrams in the bulk. After the resummation, the AdS 4-particle scattering amplitude is given in terms of a single unknown function of the spectral parameter. We then "bootstrap" the unknown function by requiring the absence of double-trace operators in the boundary OPE. Our results are at leading nontrivial order in 1 N , and include the full dependence on the quartic coupling, the mass parameters, and the AdS radius. In the bosonic O(N ) model we study both the massive phase and the symmetry-breaking phase, which exists even in AdS 2 evading Coleman's theorem, and identify the AdS analogue of a resonance in flat space. We then propose that symmetry breaking in AdS implies the existence of a conformal manifold in the boundary conformal theory. We also provide evidence for the existence of a critical point with bulk conformal symmetry, matching existing results and finding new ones for the conformal boundary conditions of the critical theories. For the Gross-Neveu model we find a bound state, which interpolates between the familiar bound state in flat space and the displacement operator at the critical point.

Section: Resultsmentioning

confidence: 99%

A study of quantum field theories in AdS at finite coupling

Carmi

Pietro

Komatsu

2019

107

191

“…Another generalization of the methods in this paper would be to consider CFTs with defects of codimension higher than two, and study how one can renormalize and classify defect fields. An example of such a model where a bulk-bulk correlator is known is the 3D Ising twist defect [45,46,47] or its generalization to O(N ) twist [48]. In this case one could consider taking the norm of the normal coordinates to zero.…”

Section: Discussionmentioning

confidence: 99%

Composite operators near the boundary

Prochazka

Söderberg

2020

Self Cite

We use renormalization group methods to study composite operators existing at a boundary of an interacting conformal field theory. In particular we relate the data on boundary operators to short-distance (near-boundary) divergences of bulk two-point functions. We further argue that in the presence of running couplings at the boundary the anomalous dimensions of certain composite operators can be computed from the relevant beta functions and remark on the implications for the boundary (pseudo) stress-energy tensor. We apply the formalism to a scalar field theory in d = 3 − dimensions with a quartic coupling at the boundary whose beta function we determine to the first non-trivial order. We study the operators in this theory and compute their conformal data using −expansion at the Wilson-Fisher fixed point of the boundary renormalization group flow. We find that the model possesses a non-zero boundary stress-energy tensor and displacement operator both with vanishing anomalous dimensions. The boundary stress tensor decouples at the fixed point in accordance with Cardy's condition for conformal invariance. We end the main part of the paper by discussing the possible physical significance of this fixed point for various values of . A. General form of a bulk-boundary correlator 32 B. Four-point correlator 33 C. Master integral 34 D. Stress-energy tensor correlator at orderĝ 35

“…It is built as a boundary condition for the tensor product of n copies of the QFT of interest -(QFT) n . In particular, the fields of consecutive copies are identified on a codimension one surface ending on the 29 Our conventions are summarized in footnote 25. location of the defect, which has therefore codimension two. Given the replica defect supported on a surface Σ lying on a constant time slice, consider the path-integral Z n (Σ) of the theory in the presence of the defect.…”

Section: The Replica Twist Defectmentioning

confidence: 99%

“…We shall also often denote the codimension as q, that is, p + q = d. The defect CFT data is constrained by crossing symmetry of the four-point function of defect primaries, and is tied to the bulk via crossing symmetry of correlators involving at least two bulk primaries [11,12]. There is a growing effort in refining our understanding of the constraints [13][14][15][16][17], extracting numerical and analytic information from them [18][19][20][21][22], and performing direct computations of correlators in specific models, see e.g., [23][24][25][26][27][28][29][30][31][32].…”

Section: Contents 1 Introduction and Summarymentioning

confidence: 99%

Universality at large transverse spin in defect CFT

Lemos

Liendo

Meineri

et al. 2018

139

We study the spectrum of local operators living on a defect in a generic conformal field theory, and their coupling to the local bulk operators. We establish the existence of universal accumulation points in the spectrum at large s, s being the charge of the operators under rotations in the space transverse to the defect. Our tools include a formula that inverts the bulk to defect OPE, analogous to the Caron-Huot formula for the four-point function [1]. Analyticity of the formula in s implies that the scaling dimensions of the defect operators are aligned in Regge trajectories ∆(s). These results require the correlator of two local operators and the defect to be bounded in a certain region, a condition that we do not prove in general. We check our conclusions against examples in perturbation theory and holography, and we make specific predictions concerning the spectrum of defect operators on Wilson lines. We also give an interpretation of the large s spectrum in the spirit of the work of Alday and Maldacena [2].