An Interacting, Higher Derivative, Boundary Conformal Field Theory

TL;DR

This paper studies a higher derivative scalar boundary conformal field theory, analyzing free and interacting cases in six dimensions, computing conformal blocks, operator dimensions, and OPE coefficients at the boundary.

Contribution

It introduces a detailed analysis of a higher derivative boundary CFT, including conformal blocks and boundary operator data at the infrared fixed point.

Findings

Conformal blocks form generalized eigenvectors of the Casimir.

Boundary operator anomalous dimensions are computed at leading order.

The theory exhibits an infrared fixed point in $d=6-\epsilon$ dimensions.

Abstract

We consider a higher derivative scalar field theory in the presence of a boundary and a classically marginal interaction. We first investigate the free limit where the scalar obeys the square of the Klein-Gordon equation. In precisely $d=6$ dimensions, modules generated by $d-2$ and $d-4$ dimensional primaries merge to form a staggered module. We compute the conformal block associated with this module and show that it is a generalized eigenvector of the Casimir operator. Next we include the effect of a classically marginal interaction that involves four scalar fields and two derivatives. The theory has an infrared fixed point in $d=6-{\epsilon}$ dimensions. We compute boundary operator anomalous dimensions and boundary OPE coefficients at leading order in the ${\epsilon}$ expansion for the allowed conformal boundary conditions.