Trace anomaly for chiral fermions via Hadamard subtraction
Abstract
We calculate the trace (conformal) anomaly for chiral fermions in a general curved background using Hadamard subtraction. While in intermediate steps of the calculation imaginary terms proportional to the Pontryagin density appear, imposing a vanishing divergence of the stress tensor these terms completely cancel, and we recover the well known result equal to half the trace anomaly of a Dirac fermion. We elaborate in detail on the advantages of the Hadamard method for the general definition of composite operators in general curved spacetimes, and speculate on possible causes for the appearance of the Pontryagin density in other calculations.
 Publication:

Journal of High Energy Physics
 Pub Date:
 October 2019
 DOI:
 10.1007/JHEP10(2019)223
 arXiv:
 arXiv:1904.10982
 Bibcode:
 2019JHEP...10..223F
 Keywords:

 Anomalies in Field and String Theories;
 Conformal and W Symmetry;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 40 pages, additional references and new appendix on twocomponent fermions