Weyl Covariance and the Energy Momentum Tensors of Higher-Derivative Free Conformal Field Theories

TL;DR

This paper explores the structure of energy momentum tensors in higher-derivative free conformal field theories, introducing algorithms for their computation, revealing geometric features, and extending analysis to spinor theories in higher dimensions.

Contribution

It presents new algorithms and compact expressions for energy momentum tensors, highlighting geometric origins and obstructions in defining them as conformal primaries in various dimensions.

Findings

Two algorithms for energy momentum tensor computation are described.

New compact expressions for energy momentum tensors are provided.

Obstructions to defining energy momentum tensors as conformal primaries are identified.

Abstract

Energy momentum tensors of higher-derivative free scalar conformal field theories in flat spacetime are discussed. Two algorithms for the computation of energy momentum tensors are described, which accomplish different goals: the first is brute-force and highlights the complexity of the energy momentum tensors, while the second displays some features of their geometric origin as variations of Weyl invariant curved-space actions. New compact expressions for energy momentum tensors are given and specific obstructions to defining them as conformal primary operators in some spacetime dimensions are highlighted. Our discussion is also extended to higher-derivative free spinor theories, which are based on higher-derivative generalizations of the Dirac action and provide interesting examples of conformal field theories in dimension higher than two.