Constraints on RG Flow for Four Dimensional Quantum Field Theories

Understand

The response of four dimensional quantum field theories to a Weyl rescaling of the metric in the presence of local couplings and which involve $a$, the coefficient of the Euler density in the energy momentum tensor trace on curved space, is reconsidered.

• Previous consistency conditions for the anomalous terms, which implicitly define a metric $G$ on the space of couplings and give rise to gradient flow like equations for $a$, are derived taking into account the role of lower dimension operators.
• The results for infinitesimal Weyl rescaling are integrated to finite rescalings $e^{2\sigma}$ to a form which involves running couplings $g_\sigma$ and which interpolates between IR and UV fixed points.
• The results are also restricted to flat space where they give rise to broken conformal Ward identities.