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Trace anomaly for chiral fermions via Hadamard subtraction

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arxiv 1904.10982 v2 pith:RRYG7MWH submitted 2019-04-24 hep-th gr-qc

classification hep-thgr-qc
keywords anomalygeneralhadamardtracechiralcurveddensityfermions
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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.

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

    hep-th 2019-08 accept novelty 6.0 of 10

    The trace anomaly of four-dimensional Weyl fermions in a non-abelian gauge background is (1/48 pi^2) tr F^2 with no parity-odd Chern-Pontryagin contribution, derived via Pauli-Villars regularization.

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