Scale and Conformal Invariance in Higher Derivative Shift Symmetric Theories

TL;DR

This paper explores the critical behavior and conformal invariance of higher derivative shift symmetric theories, classifying their critical dimensions and computing key quantum properties at leading order.

Contribution

It introduces a classification of shift symmetric theories with higher derivatives and demonstrates their conformal invariance at fixed points, including non-renormalization properties.

Findings

Two infinite families of theories are conformally invariant at fixed points.

Beta functions depend only on anomalous dimensions for cubic theories.

Explicit critical dimensions and anomalous dimensions are computed.

Abstract

The critical behavior of infinite families of shift symmetric interacting theories with higher derivative kinetic terms (non unitary) is considered. Single scalar theories with shift symmetry are classified according to their upper critical dimensions and studied at the leading non trivial order in perturbation theory. For two infinite families, one with quartic and one with cubic interactions, beta functions, criticality conditions and universal anomalous dimensions are computed. At the order considered, the cubic theories enjoy a one loop non renormalization of the vertex, so that the beta function depends non trivially only on the anomalous dimension. The trace of the energy momentum tensor is also investigated and it is shown that these two families of QFTs are conformally invariant at the fixed point of the RG flow.