Uncovering novel phase structures in Box ^k scalar theories with the renormalization group

Abstract

We present a detailed version of our recent work on the RG approach to multicritical scalar theories with higher derivative kinetic term phi (-Box )^kphi and upper critical dimension d_c = 2nk/(n-1). Depending on whether the numbers k and n have a common divisor two classes of theories have been distinguished. For coprime k and n-1 the theory admits a Wilson-Fisher type fixed point. We derive in this case the RG equations of the potential and compute the scaling dimensions and some OPE coefficients, mostly at leading order in epsilon . While giving new results, the critical data we provide are compared, when possible, and accord with a recent alternative approach using the analytic structure of conformal blocks. Instead when k and n-1 have a common divisor we unveil a novel interacting structure at criticality. Box ^2 theories with odd n, which fall in this class, are analyzed in detail. Using the RG flows it is shown that a derivative interaction is unavoidable at the critical point. In particular there is an infrared fixed point with a pure derivative interaction at which we compute the scaling dimensions and, for the particular example of Box ^2 theory in d_c=6, also some OPE coefficients.