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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2411.12934 |
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| _version_ | 1866929657943687168 |
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| author | Nakayama, Yu |
| author_facet | Nakayama, Yu |
| contents | Inspired by the possibility of emergent supersymmetry in critical random systems, we study a field theory model with a quartic potential of one superfield, possessing the Parisi-Sourlas supertranslation symmetry. Within perturbative $ε$ expansion, we find nine non-trivial scale invariant renormalization group fixed points, but only one of them is conformal. We, however, believe scale invariance without conformal invariance cannot occur without a sophisticated mechanism because it predicts the existence of a non-conserved but non-renormalized vector operator called virial current, whose existence must be non-generic. We show that the virial current in this model is related to the supercurrent by supertranslation. The supertranslation Ward-Takahashi identity circumvents the genericity argument, explaining its non-renormalization property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12934 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parisi-Sourlas Supertranslation and Scale without Conformal symmetry Nakayama, Yu High Energy Physics - Theory Disordered Systems and Neural Networks Statistical Mechanics Inspired by the possibility of emergent supersymmetry in critical random systems, we study a field theory model with a quartic potential of one superfield, possessing the Parisi-Sourlas supertranslation symmetry. Within perturbative $ε$ expansion, we find nine non-trivial scale invariant renormalization group fixed points, but only one of them is conformal. We, however, believe scale invariance without conformal invariance cannot occur without a sophisticated mechanism because it predicts the existence of a non-conserved but non-renormalized vector operator called virial current, whose existence must be non-generic. We show that the virial current in this model is related to the supercurrent by supertranslation. The supertranslation Ward-Takahashi identity circumvents the genericity argument, explaining its non-renormalization property. |
| title | Parisi-Sourlas Supertranslation and Scale without Conformal symmetry |
| topic | High Energy Physics - Theory Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2411.12934 |