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

Understand

We present a detailed version of our recent work on the renormalization group approach to multicritical scalar theories with higher derivative kinetic term of the form $\phi(-\Box)^k\phi$ 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 which show qualitatively different features.
• For coprime $k$ and $n-1$ the theory admits a Wilson-Fisher type fixed point with a marginal interaction $\phi^{2n}$.
• We derive in this case the renormalization group equations of the potential at the functional level and compute the scaling dimensions and some OPE coefficients, mostly at leading order in $\epsilon$.