Axion Wormholes and the AdS/CFT Factorization Problem

TL;DR

This paper explores the role of Euclidean and complex axion wormholes in the AdS/CFT factorization problem, analyzing their dominance and relevance depending on boundary conditions and complex contours in a 2+1 dimensional setting.

Contribution

It provides a detailed analysis of axion wormholes' relevance to the AdS/CFT factorization problem, emphasizing boundary conditions and complex contour choices.

Findings

Wormholes are subdominant near real boundary values of axion field.

Wormholes become dominant near negative imaginary boundary values.

Relevance of wormholes depends on contour choices and Stokes' lines.

Abstract

This work investigates the relevance of Euclidean and complex axion wormholes to the AdS/CFT factorization problem. We use a framework that defines bulk gravitational path integrals by integrating over a real Lorentz-signature contour and then, as needed, perhaps further analytically continuing the resulting functions of boundary conditions. For technical reasons we focus on the case of 2+1 bulk dimensions. The AdS boundary conditions (in any dimension) require us to impose Dirichlet boundary conditions on the standard Euclidean axion $\chi_E$. Fixing its asymptotic values on two boundary spheres to $\pm \chi_{E,\infty}$, we find such wormholes to be subdominant to a UV-sensitive endpoint contribution for $\chi_{E, \infty}$ near the real axis, and that (with our conventions) they become dominant only for $\chi_{E, \infty}$ near the negative imgainary axis. Furthermore, such wormholes are irrelevant to our computation for ${\rm Im} \chi_{E, \infty} >0$ (in the sense that the associated ascent contour fails to intersect the contour of integration). The relevance of the wormhole saddle for real positive $\chi_{E, \infty}$ is in fact a matter of choice, as the saddle then lies on a Stokes' line at which the relevant intersection number changes from zero to one.