Effective Field Theory of Conformal Boundaries

TL;DR

This paper develops an effective field theory for conformal boundaries and impurities, providing universal formulas for boundary structure constants and revealing constraints on Casimir energy, with implications for thermal EFT as a special case.

Contribution

It introduces a novel EFT framework for conformal impurities and boundaries, deriving universal high-energy formulas and energy constraints, unifying with thermal EFT.

Findings

Universal formulas for boundary structure constants at high energy.

Constraints on Casimir energy for conformal impurities.

Thermal EFT as a special case of the developed EFT.

Abstract

We introduce an effective field theory (EFT) for conformal impurity by considering a pair of transversely displaced impurities and integrating out modes with mass inversely proportional to the separation distance. This EFT captures the universal signature of the impurity seen by a heavy local operator. We focus on the case of conformal boundaries and derive universal formulas from this EFT for the boundary structure constants at high energy. We point out that the more familiar thermal EFT for conformal field theory is a special case of this EFT with distinguished conformal boundaries. We also derive, for general conformal impurities, non-positivity and convexity-like constraints on the Casimir energy which determines the leading EFT coefficient.