The O(N) model with φ6 potential in Double-struck capital R2 x R+

We study the largeNlimit ofO(N) scalar field theory with classically marginal phi(6)interaction in three dimensions in the presence of a planar boundary. This theory has an approximate conformal invariance at largeN. We find different phases of the theory corresponding to different boundary conditions for the scalar field. Computing a one loop effective potential, we examine the stability of these different phases. The potential also allows us to determine a boundary anomaly coefficient in the trace of the stress tensor. We further compute the current and stress-tensor two point functions for the Dirichlet case and decompose them into boundary and bulk conformal blocks. The boundary limit of the stress tensor two point function allows us to compute the other boundary anomaly coefficient. Both anomaly coefficients depend on the approximately marginal phi(6)coupling.