Two-loop renormalization of multiflavor φ3 theory in six dimensions and the trace anomaly

We use the background-field method and the heat kernel to obtain all counterterms to two-loop order of conformally coupled multiflavor phi(3) theory in six spacetime dimensions, defined in curved spacetime and with spacetime-dependent couplings. We also include spacetime-dependent mass terms for completeness. We use these results to write a general expression for the trace anomaly. With the use of Weyl consistency conditions, we are able to show that the strong a-theorem for a certain natural candidate quantity (a) over tilde is violated in this theory and obtain a three-loop expression for the coefficient a of the Euler term in the anomaly.