Scalar Three-point Functions in a CDL Background

TL;DR

This paper calculates the scalar three-point functions in a Coleman-De Luccia background, exploring their behavior near the boundary and on the past lightcone, and discusses implications for FRW-CFT correspondence.

Contribution

It provides the first detailed computation of scalar three-point functions in CDL backgrounds, including massless and massive cases, with analysis of conformal structure and limitations.

Findings

Three-point functions exhibit conformal structure near the boundary.

Massive scalar three-point functions face obstacles in extending the massless field-operator correspondence.

Results support the FRW-CFT proposal in flat FRW patches.

Abstract

Motivated by the FRW-CFT proposal by Freivogel, Sekino, Susskind and Yeh, we compute the three-point function of a scalar field in a Coleman-De Luccia instanton background. We first compute the three-point function of the scalar field making only very mild assumptions about the scalar potential and the instanton background. We obtain the three-point function for points in the FRW patch of the CDL instanton and take two interesting limits; the limit where the three points are near the boundary of the hyperbolic slices of the FRW patch, and the limit where the three points lie on the past lightcone of the FRW patch. We expand the past lightcone three-point function in spherical harmonics. We show that the near boundary limit expansion of the three-point function of a massless scalar field exhibits conformal structure compatible with FRW-CFT when the FRW patch is flat. We also compute the three-point function when the scalar is massive, and explain the obstacles to generalizing the conjectured field-operator correspondence of massless fields to massive fields.