Axial Anomaly in the $SU(N)$ Gauge Matrix Model
| Autor: | Acharyya, Nirmalendu, Pandey, Mahul, Vaidya, Sachindeo |
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| Rok vydání: | 2021 |
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| Zdroj: | Phys. Rev. Lett. 127, 092002 (2021) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevLett.127.092002 |
| Popis: | 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 $\mathbb{Z}_{4N_f}$. Comment: 17 pages, 3 figures. Typo corrected in eq. 2.15, citations corrected. This is a longer version, a shorter version will appear in the journal |
| Databáze: | arXiv |
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