A Wilsonian Energy-Momentum Tensor

TL;DR

This paper presents a method to construct the energy-momentum tensor for local conformal field theories using Wilsonian effective Lagrangians, linking renormalization group equations with conformal invariance.

Contribution

It introduces a novel approach to derive the energy-momentum tensor directly from Wilsonian effective actions, connecting renormalization group flow with conformal symmetry constraints.

Findings

Derived an explicit expression for the energy-momentum tensor in conformal field theories.

Established a single equation linking the RG flow and conformal invariance.

Demonstrated the implications of tracelessness for the energy-momentum tensor.

Abstract

For local conformal field theories, it is shown how to construct an expression for the energy-momentum tensor in terms of a Wilsonian effective Lagrangian. Tracelessness implies a single, unintegrated equation which enforces both the Exact Renormalization Group equation and its partner encoding invariance under special conformal transformations.