Anomalies at finite density and chiral fermions

Abstract

Using perturbation theory in the Euclidean (imaginary time) formalism as well as the non-perturbative Fujikawa method, we verify that the chiral anomaly equation remains unaffected in the presence of nonzero chemical potential, $μ$. We extend our considerations to fermions with exact chiral symmetry on the lattice and discuss the consequences for the recent Bloch-Wettig proposal for the Dirac operator at finite chemical potential. We propose a new simpler method of incorporating $μ$ and compare it with the Bloch-Wettig idea.

12 pages, 3 figures,some typos corrected, a better proof for the μindependence of anomaly is given in section IIB, v4: the published version