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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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-12-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP12(2024)149 |
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| author | Johanna Erdmenger Ioannis Matthaiakakis René Meyer Dmitri Vassilevich |
| author_facet | Johanna Erdmenger Ioannis Matthaiakakis René Meyer Dmitri Vassilevich |
| author_sort | Johanna Erdmenger |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7348a6c9b1a34f69a72565eeba6101f1 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-7348a6c9b1a34f69a72565eeba6101f12025-01-05T12:06:55ZengSpringerOpenJournal of High Energy Physics1029-84792024-12-0120241212110.1007/JHEP12(2024)149The chiral torsional anomaly and the Nieh-Yan invariant with and without boundariesJohanna Erdmenger0Ioannis Matthaiakakis1René Meyer2Dmitri Vassilevich3Institute for Theoretical Physics and Astrophysics, and Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat, Julius-Maximilians-Universität WürzburgMathematical Sciences and STAG Research Centre, University of SouthamptonInstitute for Theoretical Physics and Astrophysics, and Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat, Julius-Maximilians-Universität WürzburgCentro de Matemática, Computação e Cognição — Universidade Federal do ABCAbstract 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.https://doi.org/10.1007/JHEP12(2024)149Anomalies in Field and String TheoriesGauge Symmetry |
| spellingShingle | Johanna Erdmenger Ioannis Matthaiakakis René Meyer Dmitri Vassilevich The chiral torsional anomaly and the Nieh-Yan invariant with and without boundaries Journal of High Energy Physics Anomalies in Field and String Theories Gauge Symmetry |
| title | The chiral torsional anomaly and the Nieh-Yan invariant with and without boundaries |
| title_full | The chiral torsional anomaly and the Nieh-Yan invariant with and without boundaries |
| title_fullStr | The chiral torsional anomaly and the Nieh-Yan invariant with and without boundaries |
| title_full_unstemmed | The chiral torsional anomaly and the Nieh-Yan invariant with and without boundaries |
| title_short | The chiral torsional anomaly and the Nieh-Yan invariant with and without boundaries |
| title_sort | chiral torsional anomaly and the nieh yan invariant with and without boundaries |
| topic | Anomalies in Field and String Theories Gauge Symmetry |
| url | https://doi.org/10.1007/JHEP12(2024)149 |
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