On the complexity of effective theories. Seiberg-Witten theory
- 1Utrecht University
- 2University of Liverpool
- 3Harvard University
Abstract
A bstract : 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 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.
Related
- Global forms of 𝒩 = 4 theories and non-minimal Seiberg-Witten solutions
- Ricci flow of Integrable Sigma Models, Hitchin Systems and Quantum Seiberg-Witten theory
- Two Recursions for the Seiberg-Witten Prepotential: Zamolodchikov's Recursion, the AGT Correspondence and Topological Recursion on the Seiberg-Witten Curve
- Photon spheres, elliptic surfaces, and Seiberg-Witten geometry
- Seiberg dualities for quiver gauge theories
BibTeX
@article{carrascal2026complexity,
title = {{On the complexity of effective theories. Seiberg-Witten theory}},
author = {Martin Carrascal and Ferdy Ellen and Thomas W. Grimm and David Prieto},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)159},
url = {https://link.springer.com/article/10.1007/JHEP10(2026)159},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - On the complexity of effective theories. Seiberg-Witten theory
AU - Martin Carrascal
AU - Ferdy Ellen
AU - Thomas W. Grimm
AU - David Prieto
PY - 2026
DA - 2026/10/14
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)159
UR - https://link.springer.com/article/10.1007/JHEP10(2026)159
AB - A bstract : 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 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.
SN - 1029-8479
ER -