Non-local correction to the energy-momentum tensor for $\phi^{3}$ theory in six dimensions

TL;DR

This paper computes the leading-order non-local quantum correction to the energy-momentum tensor in six-dimensional $\,\phi^3$ theory, revealing modifications to the virial current when coupled to gravity, with implications for conformal invariance.

Contribution

The paper explicitly derives the non-local quantum correction to the energy-momentum tensor in six-dimensional $\,\phi^3$ theory using the background field method, highlighting its impact on the virial current.

Findings

Non-local correction modifies the virial current in the energy-momentum tensor.

Correction affects the traceless part in classically Weyl-invariant scenarios.

Explicit computation of quantum corrections in six-dimensional scalar theory.

Abstract

Applying the background field method, we construct by explicit computation the leading-order non-local quantum correction to the on-shell effective action for $\phi^3$ theory in six dimensions. We then use the resulting action to obtain the non-local correction to the energy-momentum tensor. At leading order, we find that this non-local correction modifies the virial current when the scalar field is minimally coupled to gravity. This is to be compared to the classically Weyl invariant case, where it only corrects the traceless part of the energy-momentum tensor.