The chiral torsional anomaly and the Nieh-Yan invariant with and without boundaries
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910633076719616 |
|---|---|
| author | Erdmenger, Johanna Matthaiakakis, Ioannis Meyer, René Vassilevich, Dmitri |
| author_facet | Erdmenger, Johanna Matthaiakakis, Ioannis Meyer, René Vassilevich, Dmitri |
| contents | 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06766 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The chiral torsional anomaly and the Nieh-Yan invariant with and without boundaries Erdmenger, Johanna Matthaiakakis, Ioannis Meyer, René Vassilevich, Dmitri High Energy Physics - Theory Mesoscale and Nanoscale Physics 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. |
| title | The chiral torsional anomaly and the Nieh-Yan invariant with and without boundaries |
| topic | High Energy Physics - Theory Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2409.06766 |