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Axial Anomaly in SU (N) Yang-Mills Matrix Models

Acharyya, N and Pandey, M and Vaidya, S (2021) Axial Anomaly in SU (N) Yang-Mills Matrix Models. In: Physical Review Letters, 127 (9).

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Official URL: https://doi.org/10.1103/PhysRevLett.127.092002


The SU(N) Yang-Mills matrix model admits self-dual and anti-self-dual instantons. When coupled to Nf flavors of massless quarks, the Euclidean Dirac equation in an instanton background has n+ positive and n- negative chirality zero modes. The vacua of the gauge theory are N-dimensional representations of SU(2), and the (anti-) self-dual instantons tunnel between two commuting representations, the initial one composed of r0(1) irreps and the final one with r0(2) irreps. We show that the index (n+-n-) in such a background is equal to a new instanton charge Tnew=±r0(2)-r0(1). Thus Tnew=(n+-n-) is the matrix model version of the Atiyah-Singer index theorem. Further, we show that the path integral measure is not invariant under a chiral rotation, and relate the noninvariance of the measure to the index of the Dirac operator. Axial symmetry is broken anomalously, with the residual symmetry being a finite group. For Nf fundamental fermions, this residual symmetry is Z2Nf, whereas for adjoint quarks it is Z4Nf. © 2021 authors. Published by the American Physical Society. Funded by SCOAP3.

Item Type: Journal Article
Publication: Physical Review Letters
Publisher: American Physical Society
Additional Information: The copyright for this article belongs to Authors
Keywords: Elementary particles; Linear equations, Axial symmetry; Chiral rotations; Dimensional representation; Dirac equations; Dirac operators; Finite groups; Index theorem; Path integral, Quantum theory
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 02 Dec 2021 12:59
Last Modified: 02 Dec 2021 12:59
URI: http://eprints.iisc.ac.in/id/eprint/70081

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