The chiral torsional anomaly and the Nieh-Yan invariant with and without boundaries
Abstract There exists a long-standing debate regarding the torsion contribution to the 4d chiral anomaly of a Dirac fermion. Central to this debate is the Nieh-Yan anomaly, which has been considered ill-defined and a regularization artifact. Using a heat-kernel approach, we examine the relationship...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-12-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP12(2024)149 |
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| Summary: | Abstract There exists a long-standing debate regarding the torsion contribution to the 4d chiral anomaly of a Dirac fermion. Central to this debate is the Nieh-Yan anomaly, which has been considered ill-defined and a regularization artifact. Using a heat-kernel approach, we examine the relationship between the Dirac operator index, the Nieh-Yan invariant and the torsional anomaly. We show the Nieh-Yan invariant vanishes on spacetimes without boundaries, if the Dirac index is well-defined. In the known examples of non-vanishing Nieh-Yan invariant on manifolds without boundaries, the heat kernel expansion breaks down, making the index ill-defined. Finally, for finite boundaries we identify several finite bulk and boundary anomaly terms, alongside bulk and boundary Nieh-Yan terms. We construct explicit counterterms that cancel the Nieh-Yan terms and argue that the boundary terms give rise to a torsional anomalous Hall effect. Our results emphasize the importance of renormalization conditions, as these can affect the non-thermal Nieh-Yan anomaly coefficients. In addition, we demonstrate that anomalous torsional transport may arise even without relying on the Nieh-Yan invariant. |
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| ISSN: | 1029-8479 |