Vacuum Decay in CFT and the Riemann-Hilbert problem

TL;DR

This paper investigates vacuum decay in 1+1D conformal field theories with background fields, revealing that the decay rate is characterized by a non-local two-form linked to Riemann-Hilbert problems, including a novel gravitational extension.

Contribution

It introduces a new non-local two-form to describe vacuum decay rates in CFTs, connecting it to Riemann-Hilbert decompositions and extending to gravitational backgrounds.

Findings

Vacuum decay rate expressed as a non-local two-form.

Boundary term added to effective Lagrangian for decay rate.

Riemann-Hilbert decomposition used for background gauge fields.

Abstract

We study vacuum stability in 1+1 dimensional Conformal Field Theories with external background fields. We show that the vacuum decay rate is given by a non-local two-form. This two-form is a boundary term that must be added to the effective in/out Lagrangian. The two-form is expressed in terms of a Riemann-Hilbert decomposition for background gauge fields, and its novel "functional" version in the gravitational case.