Abstract
Applying the background field method, we construct by explicit computation the leading-order nonlocal quantum correction to the on-shell effective action for $$\phi ^3$$ theory in six dimensions. We then use the resulting action to obtain the nonlocal correction to the energy-momentum tensor. At leading order, we find that this nonlocal 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.
Highlights
Energy and momentum are two very important quantities in physics
To study the energy-momentum tensor, it is convenient to consider a quantum field theory of interest in a general curved background since the energy-momentum tensor is naturally defined as the composite field that is conjugate to the background metric
Φ3 theory is not an interesting theory from the phenomenological point of view, it serves as an intriguing theoretical model for one to probe and gain a deeper insight into the nature of quantum field theory
Summary
Energy and momentum are two very important quantities in physics. In most field theories, the densities of these two quantities can be concisely described by one object, the energy-momentum tensor; it plays a crucial role associated with the global symmetries of a theory. Following the procedure laid out in [12], we construct the quantum effective action for φ3 theory within the context of perturbation theory, and show by explicit computation that while the correction to the trace of the energy-momentum tensor is local and of order λ3, the leading-order nonlocal energy-momentum tensor is of order λ2. To our knowledge, these results have not been presented in the literature, and one goal of this work is to fill this gap. Useful integrals needed for our computations are listed in Appendix A
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