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Heavy holographic correlators in defect conformal field theories

Georgios Linardopoulos, Chanyong Park

TL;DR

This work analyzes holographic defect CFTs using a bottom-up AdS/CFT framework with a codimension-1 probe brane, focusing on heavy scalar operators. It demonstrates that the brane embedding reproduces known top-down results and enables the computation of defect one- and two-point functions at strong coupling via geodesic approximations, including across-defect, reflected, and ambient-channel correlators. The results for heavy operators align with the boundary-operator expansion and the operator product expansion in appropriate double-scaling limits, supporting a universal structure of heavy defect correlators. The study highlights the potential universality of these geodesic-based results across different codimension-1 defects and outlines directions toward higher codimensions and spinorial operators.

Abstract

We study holographic defect conformal field theories which are dual to probe branes with bottom-up methods. First we determine the embedding of codimension-1 probe branes in AdS space. Then we compute defect one and two-point correlation functions of heavy scalar operators at strong coupling. In particular, we use geodesic approximations to compute scalar two-point functions across the defect, reflected two-point functions, and ambient channel two-point functions. In appropriate limits, our results agree with the boundary operator expansion (BOE) and the operator product expansion (OPE).

Heavy holographic correlators in defect conformal field theories

TL;DR

This work analyzes holographic defect CFTs using a bottom-up AdS/CFT framework with a codimension-1 probe brane, focusing on heavy scalar operators. It demonstrates that the brane embedding reproduces known top-down results and enables the computation of defect one- and two-point functions at strong coupling via geodesic approximations, including across-defect, reflected, and ambient-channel correlators. The results for heavy operators align with the boundary-operator expansion and the operator product expansion in appropriate double-scaling limits, supporting a universal structure of heavy defect correlators. The study highlights the potential universality of these geodesic-based results across different codimension-1 defects and outlines directions toward higher codimensions and spinorial operators.

Abstract

We study holographic defect conformal field theories which are dual to probe branes with bottom-up methods. First we determine the embedding of codimension-1 probe branes in AdS space. Then we compute defect one and two-point correlation functions of heavy scalar operators at strong coupling. In particular, we use geodesic approximations to compute scalar two-point functions across the defect, reflected two-point functions, and ambient channel two-point functions. In appropriate limits, our results agree with the boundary operator expansion (BOE) and the operator product expansion (OPE).
Paper Structure (17 sections, 4 figures, 1 table)

This paper contains 17 sections, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. One-point functions
  3. Top-down approach
  4. Chiral primary operators
  5. One-point function (weak coupling)
  6. Holographic description
  7. One-point function (strong coupling)
  8. Bottom-up approach
  9. One-point function (strong coupling)
  10. Two-point functions
  11. Two-point function across the defect
  12. Reflected two-point functions
  13. Collinear case ($\textbf{x} = \textbf{y}$)
  14. Equidistant case ($x_3 = y_3$)
  15. Ambient channel two-point functions
  16. ...and 2 more sections

Figures (4)

  • Figure 1: Interface brane in the bottom-up model.
  • Figure 2: Crossing equation in codimension-1 dCFT.
  • Figure 3: Reflected two-point functions for (a) $\textbf{x} = \textbf{y}$ (collinear) and (b) $x_3 = y_3$ (equidistant).
  • Figure 4: Ambient channel two-point function of defect CFT.