Conformal constraints on defects

TL;DR

This paper explores how conformal invariance constrains defects in conformal field theories, introducing defect expansion and solving related conformal blocks to understand defect correlations.

Contribution

It identifies a class of defects invariant under conformal transformations and develops the defect expansion framework, generalizing boundary state concepts.

Findings

Correlation functions are fixed up to a constant by conformal invariance.

Derived differential equations for conformal blocks of defects.

Solved conformal blocks in specific cases.

Abstract

In this paper we study the constraints imposed by conformal invariance on extended objects a.k.a defects in a conformal field theory. We identify a particularly nice class of defects that is closed under conformal transformations. Correlation function of the defect with a bulk local operator is fixed by conformal invariance up to an overall constant. This gives rise to the notion of defect expansion, where the defect itself is expanded in terms of local operators. This expansion generalizes the idea of the boundary state. We will show how one can fix the correlation function of two defects from the knowledge of the defect expansion. The defect correlator admits a number of conformal cross-ratios depending on their dimensionality. We find the differential equation obeyed by the conformal block and solve them in certain special cases.