Weighted scale invariant quantum field theories

TL;DR

This paper explores a class of Lorentz violating quantum field theories with higher space derivatives that are renormalizable and exhibit weighted scale invariance, providing new examples of such theories with detailed analysis.

Contribution

It introduces and classifies weighted scale invariant quantum field theories with higher space derivatives, including explicit models and their correlation functions in four dimensions.

Findings

Existence of Lorentz violating fixed points in various dimensions

Explicit calculation of correlation functions and critical exponents in 4D models

Construction of RG flows between fixed points

Abstract

We study a class of Lorentz violating quantum field theories that contain higher space derivatives, but no higher time derivatives, and become renormalizable in the large N expansion. The fixed points of their renormalization-group flows provide examples of exactly "weighted scale invariant" theories, which are noticeable Lorentz violating generalizations of conformal field theories. We classify the scalar and fermion models that are causal, stable and unitary. Solutions exist also in four and higher dimensions, even and odd. In some explicit four dimensional examples, we compute the correlation functions to the leading order in 1/N and the critical exponents to the subleading order. We construct also RG flows interpolating between pairs of fixed points.