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arXiv · 2104.04048

Axial Anomaly in the $SU(N)$ Gauge Matrix Model

Nirmalendu Acharyya·Mahul Pandey·Sachindeo Vaidya
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Abstract

The $SU(N)$ Yang-Mills matrix model admits self-dual and anti-self-dual instantons. When coupled to $N_f$ flavors of massless quarks, the Euclidean Dirac equation in an instanton background has $n_+$ positive and $n_-$ negative chirality zero modes. We show that the index $(n_+ - n_-)$ is equal to a suitably defined instanton charge. Further, we show that the path integral measure is not invariant under a chiral rotation, and relate the non-invariance of the measure to the index of the Dirac operator. Axial symmetry is broken anomalously, with the residual symmetry being a finite group. For $N_f$ fundamental fermions, this residual symmetry is $\mathbb{Z}_{2N_f}$, whereas for adjoint quarks it is $\mathbb{Z}_{4N_f}$.

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Nirmalendu Acharyya, Mahul Pandey, Sachindeo Vaidya. 2021-04-08. Axial Anomaly in the $SU(N)$ Gauge Matrix Model. https://doi.org/10.1103/physrevlett.127.092002

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