Higher loops in AdS: applications to boundary CFT

TL;DR

This paper uses higher-loop calculations in AdS space to analyze boundary conformal field theories related to the critical O(N) model, providing detailed conformal data and estimates for boundary central charges in three dimensions.

Contribution

It performs higher-loop computations in AdS to extract BCFT observables for the critical O(N) model, advancing understanding of boundary effects in conformal field theories.

Findings

Determined the free energy to four-loop order in the ordinary universality class.

Computed the one-point function of the lightest O(N) singlet operator to three-loop order.

Estimated the boundary central charge in three dimensions using Padé approximants.

Abstract

The Euclidean Anti-de Sitter (AdS) space provides a natural framework for studying boundary conformal field theory (BCFT). We analyze the conformal boundary conditions of the critical O$(N)$ model in $d=4-\epsilon$ dimensions using the $\epsilon$-expansion, and extract some BCFT observables through higher-loop calculations in AdS. Specifically, in the so-called "ordinary" universality class, we determine the free energy to four-loop order and the one-point function of the lightest O$(N)$ singlet operator to three-loop order. In the symmetry breaking "normal" universality class, we derive the two-loop free energy and compute the leading correction to the one-point function of the lightest O($N$) vector. We apply Pad\'e approximants to extract the corresponding conformal data in three dimensions. In particular, from a suitable dimensional continuation of the free energy in AdS, we obtain estimates for the boundary central charge of the BCFT in $d=3$.