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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2404.18138 |
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| _version_ | 1866929330000494592 |
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| author | Sato, Yotaro |
| author_facet | Sato, Yotaro |
| contents | In this thesis, we propose a new consistency condition of quantum field theory: Having an odd number of Majorana fermion zero modes on a dynamical point-like soliton signifies an inconsistency in a theory with 3+1 or higher dimensions. This inconsistency is related to the non-perturbative anomaly in known models of quantum field theory. As an application, we check the consistency of string and M theory compactifications with branes. We propose a new criterion on the consistency of brane configurations: An odd number of Majorana fermion zero modes on a D-brane stretching infinitely in space is acceptable, whereas compactifying it to a point-like object leads to an inconsistency. We show that a single M5-brane always has an even number of Majorana fermion zero modes because of the symmetry on the worldvolume in 2+1 or higher dimensional compactifications of M-theory. We also construct models with an odd number of Majorana fermion zero modes by intersecting D-branes. From our criterion, compactifying such branes to point-like objects is not allowed. Finally, we show that the gauge invariance on the intersecting branes always requires an even number of Majorana fermion zero modes on a point-like brane. This observation gives another interpretation of the inconsistency we introduced. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18138 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Majorana Fermion Zero Modes and Anomalies in String and M Theories Sato, Yotaro High Energy Physics - Theory In this thesis, we propose a new consistency condition of quantum field theory: Having an odd number of Majorana fermion zero modes on a dynamical point-like soliton signifies an inconsistency in a theory with 3+1 or higher dimensions. This inconsistency is related to the non-perturbative anomaly in known models of quantum field theory. As an application, we check the consistency of string and M theory compactifications with branes. We propose a new criterion on the consistency of brane configurations: An odd number of Majorana fermion zero modes on a D-brane stretching infinitely in space is acceptable, whereas compactifying it to a point-like object leads to an inconsistency. We show that a single M5-brane always has an even number of Majorana fermion zero modes because of the symmetry on the worldvolume in 2+1 or higher dimensional compactifications of M-theory. We also construct models with an odd number of Majorana fermion zero modes by intersecting D-branes. From our criterion, compactifying such branes to point-like objects is not allowed. Finally, we show that the gauge invariance on the intersecting branes always requires an even number of Majorana fermion zero modes on a point-like brane. This observation gives another interpretation of the inconsistency we introduced. |
| title | Majorana Fermion Zero Modes and Anomalies in String and M Theories |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.18138 |