Vacuum decay in CFT and the Riemann–Hilbert problem

We study vacuum stability in 1+11+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.