TY - JOUR

T1 - Axial U(1) anomaly in a gravitational field via the gradient flow

AU - Morikawa, Okuto

AU - Suzuki, Hiroshi

N1 - Funding Information:
This work was originally planned to be presented at the commemorative lecture for the Yukawa–Kimura prize of 2017. The work of H.S. is supported in part by a Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research Grant Number JP16H03982.
Publisher Copyright:
© The Author(s) 2018. Published by Oxford University Press on behalf of the Physical Society of Japan.

PY - 2018/7/1

Y1 - 2018/7/1

N2 - 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.

AB - 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.

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U2 - 10.1093/ptep/pty073

DO - 10.1093/ptep/pty073

M3 - Article

AN - SCOPUS:85057747994

VL - 2018

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

SN - 2050-3911

IS - 7

M1 - 073B02

ER -