Holographic correlation functions from wedge

TL;DR

This paper introduces a new holographic approach for computing correlation functions of heavy operators in conformal field theories using excised geometries and backreacted bulk solutions, with results validated against previous methods.

Contribution

It develops a refined holographic method for heavy operators, utilizing excised geometries and backreacted solutions, expanding the toolkit for AdS/CFT computations.

Findings

Correlation functions derived from excised geometries match numerical and perturbative calculations.

Backreacted geometries reproduce correlation functions accurately, despite differences from Fefferman-Graham gauge.

Discrepancies with FG gauge are confirmed and explained through additional examples.

Abstract

In this work, we propose a novel holographic method for computing correlation functions of operators in conformal field theories. This method refines previous approaches and is specifically aimed at being applied to heavy operators. For operators that correspond to particles in the bulk, we show that the correlation functions can be derived from the on-shell actions of excised geometries for heavy operators, using numerical and perturbative calculations. These excised geometries are constructed from various background solutions such as \Poincare AdS$_3$, global AdS$_3$, and BTZ by cutting out a wedge bounded by two intersecting End-of-the-world branes and the AdS boundary. The wedge itself can be interpreted as a dual to a BCFT with cusps in the AdS/BCFT framework. Additionally, we calculate the correlation functions for heavy operators directly by constructing backreacted bulk geometries for particle excitations through coordinate transformations from a conical solution. We find that the on-shell actions of these backreacted solutions accurately reproduce correlation functions, although they differ from those computed in Fefferman-Graham(FG) gauge. This discrepancy, previously noted and explained in our earlier work, is reinforced by additional examples presented here.