Weyl fermions in a non-abelian gauge background and trace anomalies

Abstract

We study the trace and chiral anomalies of Weyl fermions in a nonabelian gauge background in four dimensions. Using a Pauli-Villars regularization we identify the trace anomaly, proving that it can be cast in a gauge invariant form, even in the presence of the non-abelian chiral anomaly, that we rederive to check the consistency of our methods. In particular, we find that the trace anomaly does not contain any parity-odd topological contribution, whose presence has been debated in the recent literature.

CP-violating supersymmetry anomaly

“…Im(c) 9π 2 F mn F mn + gravitino (21) They are in agreement with [25]. When c is real, it reproduces the results in [32] (with corrections made in [33]).…”

“…Some time ago, it was suggested that in addition to the Euler density and the Weyl tensor squared, the CP-violating Pontryagin density can appear in the Weyl anomaly [12]. There have been some discussions on the explicit demonstration of the Pontryagin density in the Weyl anomaly in [13][14][15][16][17][18][19][20][21][22][23][24]. In our recent paper [25], we have found that the supersymmetric extension of the CP-violating Weyl anomaly can be consistently formulated.…”

Axial gravity and anomalies of fermions

“…[4] and [20]. The analogous case of a Weyl fermion in a gauge background has also been studied more recently in [5,12], where it was found that parity-odd terms do not contribute to the trace anomaly in that context as well.…”

“…This method has already been applied successfully to several contexts in the past, as the case of two-dimensional b-c systems [10], which bear some analogies to the four-dimensional Weyl fermion case, or the more exotic model of chiral bosons [11]. It is the same method used more recently in [4,5,12] to address the trace anomalies of a Weyl fermion.…”

Trace anomaly for Weyl fermions using the Breitenlohner-Maison scheme for γ*

“…However, with strictly four-dimensional regularization methods such as Pauli-Villars regularization [7,8] employed by Bastianelli et al, or Hadamard subtraction used by Zahn and the last author [9], CP-odd terms in the trace anomaly do not arise at all. In between, this has given rise to more general discussions involving gauge anomalies [10,11] and general CP-violating theories [12,13]. Apart from the natural consequences this may have in the building of the Standard Model and extensions thereof, there will also be repercussions in our understanding of the early universe [14][15][16].…”