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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.11029 |
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| _version_ | 1866912759629742080 |
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| author | Carrascal, Martin Ellen, Ferdy Grimm, Thomas W. Prieto, David |
| author_facet | Carrascal, Martin Ellen, Ferdy Grimm, Thomas W. Prieto, David |
| contents | Motivated by the idea that consistent quantum field theories should admit a finite description, we investigate the complexity of effective field theories using the framework of effective o-minimality. Our focus is on quantifying the geometric and logical information required to describe moduli spaces and quantum-corrected couplings. As a concrete setting, we study pure $\mathcal{N}=2$ super-Yang-Mills theory along its quantum moduli space using Seiberg-Witten elliptic curves. We argue that the complexity computation should be organized in terms of local cells that cover the near-boundary regions where additional states become light, each associated with an appropriate duality frame. These duality frames are crucial for keeping the global complexity finite: insisting on a single frame extending across all such limits would yield a divergent complexity measure. This case study illustrates how tame geometry uses dualities to yield finite-complexity descriptions of effective theories and points towards a general framework for quantifying the complexity of the space of effective field theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11029 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Complexity of Effective Theories -- Seiberg-Witten theory Carrascal, Martin Ellen, Ferdy Grimm, Thomas W. Prieto, David High Energy Physics - Theory Motivated by the idea that consistent quantum field theories should admit a finite description, we investigate the complexity of effective field theories using the framework of effective o-minimality. Our focus is on quantifying the geometric and logical information required to describe moduli spaces and quantum-corrected couplings. As a concrete setting, we study pure $\mathcal{N}=2$ super-Yang-Mills theory along its quantum moduli space using Seiberg-Witten elliptic curves. We argue that the complexity computation should be organized in terms of local cells that cover the near-boundary regions where additional states become light, each associated with an appropriate duality frame. These duality frames are crucial for keeping the global complexity finite: insisting on a single frame extending across all such limits would yield a divergent complexity measure. This case study illustrates how tame geometry uses dualities to yield finite-complexity descriptions of effective theories and points towards a general framework for quantifying the complexity of the space of effective field theories. |
| title | On the Complexity of Effective Theories -- Seiberg-Witten theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.11029 |