Eur. Phys. J. C (2023) 83: 839
https://doi.org/10.1140/epjc/s10052-023-11984-z

Regular Article - Theoretical Physics

CFT correlators and CP-violating trace anomalies

¹ Dipartimento di Matematica e Fisica, Università del Salento and INFN Sezione di Lecce, Via Arnesano, 73100, Lecce, Italy
² National Center for HPC, Big Data and Quantum Computing, Casalecchio di Reno, Italy
³ Institute for Theoretical Physics (ITP), University of Heidelberg, Philosophenweg 16, 69120, Heidelberg, Germany

^b stefano.lionetti@unisalento.it

Received: 11 July 2023
Accepted: 26 August 2023
Published online: 22 September 2023

Abstract

We analyze the parity-odd correlators ${⟨JJO⟩}_{\mathit{odd}},$${⟨JJT⟩}_{\mathit{odd}},$${⟨TTO⟩}_{\mathit{odd}}$ and ${⟨TTT⟩}_{\mathit{odd}}$ in momentum space, constrained by conformal Ward identities, extending our former investigation of the parity-odd chiral anomaly vertex. We investigate how the presence of parity-odd trace anomalies affect such correlators. Motivations for this study come from holography, early universe cosmology and from a recent debate on the chiral trace anomaly of a Weyl fermion. In the current CFT analysis, O can be either a scalar or a pseudoscalar operator and it can be identified with the trace of the stress–energy tensor. We find that the ${⟨JJO⟩}_{\mathit{odd}}$ and ${⟨TTO⟩}_{\mathit{odd}}$ can be different from zero in a CFT. This occurs when the conformal dimension of the scalar operator is ${\mathrm{\Delta }}_3=4,$ as in the case of $O=T_{\mu }^{\mu }.$ Moreover, if we assume the existence of parity-odd trace anomalies, the conformal ${⟨JJT⟩}_{\mathit{odd}}$ and ${⟨TTT⟩}_{\mathit{odd}}$ are nonzero. In particular, in the case of ${⟨JJT⟩}_{\mathit{odd}}$ the transverse–traceless component is constrained to vanish, and the correlator is determined only by the trace part with the anomaly pole.