https://doi.org/10.1140/epjc/s10052-021-09523-9
Regular Article - Theoretical Physics
The conformal anomaly action to fourth order (4T) in 
in momentum space
1
Dipartimento di Matematica e Fisica, Università del Salento and INFN Sezione di Lecce, Via Arnesano, 73100, Lecce, Italy
2
Galileo Galilei Institute for Theoretical Physics, Largo Enrico Fermi 2, 50125, Florence, Italy
b
matteomaria.maglio@le.infn.it
Received:
30
March
2021
Accepted:
2
August
2021
Published online:
16
August
2021
We elaborate on the structure of the conformal anomaly effective action up to 4-th order, in an expansion in the gravitational fluctuations (h) of the background metric, in the flat spacetime limit. For this purpose we discuss the renormalization of 4-point functions containing insertions of stress-energy tensors (4T), in conformal field theories in four spacetime dimensions with the goal of identifying the structure of the anomaly action. We focus on a separation of the correlator into its transverse/traceless and longitudinal components, applied to the trace and conservation Ward identities (WI) in momentum space. These are sufficient to identify, from their hierarchical structure, the anomaly contribution, without the need to proceed with a complete determination of all of its independent form factors. Renormalization induces sequential bilinear graviton-scalar mixings on single, double and multiple trace terms, corresponding to 
interactions of the scalar curvature, with intermediate virtual massless exchanges. These dilaton-like terms couple to the conformal anomaly, as for the chiral anomalous WIs. We show that at 4T level a new traceless component appears after renormalization. We comment on future extensions of this result to more general backgrounds, with possible applications to non local cosmologies.
This work is dedicated to the memory of Theodore Tomaras.
© The Author(s) 2021
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3
