Energy momentum tensor correlators in $\phi^4$ theory II: The spin-two sector

TL;DR

This paper computes the four-loop corrections to the energy-momentum tensor correlator in $\,\,\phi^4$ theory, revealing a new RG-sector contribution and demonstrating an eigenvalue-like equation for the C_T charge, with potential applications.

Contribution

It introduces the RG-sector correction to the C_T charge at four loops and shows that C_T satisfies an eigenvalue-like equation, extending previous work to higher loops.

Findings

Decomposition of C_T into conformal and RG sectors.

Identification of a new RG-sector correction proportional to the beta-function.

C_T satisfies an eigenvalue-like equation with a different eigenvalue.

Abstract

We extend the computation of the C_T charge of the 2-point function of the Energy-Momentum Tensor to 4-loops. We show that C_T decomposes into two sectors, the conformal sector, which encodes the value of the central charge at fixed points and an RG-sector that contains logarithmic and constant corrections proportional to the beta-function. This latter constitutes the main new result of this work and is inaccessible via CFT methods alone. Furthermore, we demonstrate that C_T satisfies an eigenvalue-like equation analogous to that of the spin-0 charge, as discussed in part I, though with a different in general eigenvalue. Finally we present three possible applications.