Trace Anomaly in Metric-Affine Gravity

by Yuichi Miyashita

Thursday 7 Nov 2024, 16:00 → 18:00 Asia/Seoul

447-1

The trace anomaly is an important result of quantum field theory in curved spacetime. We usually use the heat kernel method to evaluate a one-loop effective action and the trace anomaly. In this talk, we explore the trace anomaly in a general metric-affine gravity geometry that includes torsion and nonmetricity. The core of the heat kernel method is the coefficients in the asymptotic expansion of the trace of the heat operator. We introduce Seeley's algorithm which provides the systematic approach to computing these coefficients for any spacetime, including nonmetricity and torsion. We then find the corrections to the trace anomaly at the one-loop level in the scaling-invariant scalar field theories under conformal, rescaling, and projective transformations. We demonstrate that invariance under the frame rescaling transformation results in an anomaly in the relationship between the hypermomentum and the stress-energy tensor. In contrast, we show that there is no anomaly under the projective transformation.
This talk is mainly based on the paper arXiv:2409.05499 [gr-qc].