A regularization-independent universal formula for the energy-momentum tensor in gauge theory in the flat spacetime can be written down by employing the so-called Yang-Mills gradient flow. We examine a possible use of the formula in the calculation of the axial U(1) anomaly in a gravitational field, the anomaly first obtained by Toshiei Kimura [Prog. Theor. Phys. 42, 1191 (1969)]. As a general argument indicates, the formula reproduces the correct non-local structure of the (axial U(1) current)-(energy-momentum tensor)-(energy-momentum tensor) triangle diagram in a way that is consistent with the axial U(1) anomaly. On the other hand, the formula does not automatically reproduce the general coordinate (or translation) Ward-Takahashi relation, requiring corrections by local counterterms. This analysis thus illustrates the fact that the universal formula as it stands can be used only in on-shell correlation functions, in which the energy-momentum tensor does not coincide with other composite operators in coordinate space.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)