The a-theorem for the four-dimensional vector model

The discussion of renormalization group flows in four-dimensional conformal field theories has recently focused on the $a$-anomaly. It has been shown that there is a monotonic decreasing function which interpolates between the ultraviolet and infrared fixed points such that $\Delta a=a_{UV}-a_{IR}>0$. In that context Komargodski and Schwimmer showed that $\Delta a$ could be studied by means of dilaton-dilaton scattering. In this paper we examine the $a$-theorem using these methods for a four-dimensional interacting theory: the O(N) vector model, considered to leading order in the 1/N expansion and all orders in the coupling constant $\lambda$.