Unleash $Q$! Cohomology, Localization, and Interpolation in Parisi-Sourlas Supersymmetry
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912772591190016 |
|---|---|
| author | Floch, Bruno Le Patashuri, Gela Trevisani, Emilio |
| author_facet | Floch, Bruno Le Patashuri, Gela Trevisani, Emilio |
| contents | Parisi--Sourlas supersymmetric models are known to undergo dimensional reduction; that is, their physics is captured by models in two fewer dimensions. In this work, we revisit dimensional reduction, providing new arguments and reformulating existing proofs in terms of the cohomology of a supercharge $Q$. We obtain three main results. First, we show that the recently developed picture of dimensional reduction via decoupling of operators admits a natural explanation in terms of $Q$-exactness. Second, we provide a new proof of dimensional reduction using the supersymmetric localization argument. Third, we revisit Cardy's ``interpolation'' proof -- which is reminiscent of localization but does not rely on saddle-point methods -- and show that it can be understood as a consequence of deforming the action by a $Q$-exact term. Finally, we show that while existing nonperturbative proofs of dimensional reduction apply only to scalar Lagrangians, our formulation of Cardy's argument extends to any theory with Parisi--Sourlas supersymmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15899 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unleash $Q$! Cohomology, Localization, and Interpolation in Parisi-Sourlas Supersymmetry Floch, Bruno Le Patashuri, Gela Trevisani, Emilio High Energy Physics - Theory Disordered Systems and Neural Networks Statistical Mechanics Parisi--Sourlas supersymmetric models are known to undergo dimensional reduction; that is, their physics is captured by models in two fewer dimensions. In this work, we revisit dimensional reduction, providing new arguments and reformulating existing proofs in terms of the cohomology of a supercharge $Q$. We obtain three main results. First, we show that the recently developed picture of dimensional reduction via decoupling of operators admits a natural explanation in terms of $Q$-exactness. Second, we provide a new proof of dimensional reduction using the supersymmetric localization argument. Third, we revisit Cardy's ``interpolation'' proof -- which is reminiscent of localization but does not rely on saddle-point methods -- and show that it can be understood as a consequence of deforming the action by a $Q$-exact term. Finally, we show that while existing nonperturbative proofs of dimensional reduction apply only to scalar Lagrangians, our formulation of Cardy's argument extends to any theory with Parisi--Sourlas supersymmetry. |
| title | Unleash $Q$! Cohomology, Localization, and Interpolation in Parisi-Sourlas Supersymmetry |
| topic | High Energy Physics - Theory Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2512.15899 |