An Interacting, Higher Derivative, Boundary Conformal Field Theory

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.