Bootstrapping boundary-localized interactions II: Minimal models at the boundary

TL;DR

This paper investigates non-trivial boundary conditions for a 3D free scalar field, combining perturbative and numerical bootstrap methods to identify new boundary fixed points and universal spectral bounds.

Contribution

It introduces a new class of boundary conditions linked to minimal models and uses both analytical and numerical techniques to explore their properties.

Findings

Existence of boundary fixed points perturbatively for large m

Numerical bootstrap reveals a sharp kink matching perturbative predictions

Universal spectral bounds for boundary conditions of the free scalar field

Abstract

We provide evidence for the existence of non-trivial unitary conformal boundary conditions for a three-dimensional free scalar field, which can be obtained via a coupling to the m'th unitary diagonal minimal model. For large m we can demonstrate the existence of the fixed point perturbatively, and for smaller values we use the numerical conformal bootstrap to obtain a sharp kink that smoothly matches onto the perturbative predictions. The wider numerical analysis also yields universal bounds for the spectrum of any other boundary condition for the free scalar field. A second kink in these bounds hints at a second class of non-standard boundary conditions, as yet unidentified.