Six-dimensional ultraviolet completion of the CP(N) σ model at two loops

We extend the recent one-loop analysis of the ultraviolet completion of the CP(N) nonlinear sigma model in six dimensions to two-loop order in the (MS) over bar scheme for an arbitrary covariant gauge. In particular we compute the anomalous dimensions of the fields and beta-functions of the four coupling constants. We note that like Quantum Electrodynamics (QED) in four dimensions the matter field anomalous dimension only depends on the gauge parameter at one loop. As a nontrivial check we verify that the critical exponents derived from these renormalization group functions at the Wilson-Fisher fixed point are consistent with the epsilon expansion of the respective large N exponents of the underlying universal theory. Using the Ward-Takahashi identity we deduce the three-loop (MS) over bar renormalization group functions for the six-dimensional ultraviolet completeness of scalar QED.