Factorized Quantum Curves and Voronoi Polytopes in 3D Duality Cascades with FI Parameters

High Energy Physics - Theory [Submitted on 18 Jun 2026] Title:Factorized Quantum Curves and Voronoi Polytopes in 3D Duality Cascades with FI Parameters View PDF HTML (experimental)Abstract:In the study of duality cascades in three-dimensional gauge theories without FI parameters, an important role is played by a fundamental domain whose vertices correspond to brane configurations with vanishing relative ranks. Through the Fermi gas formalism, such brane configurations are known to be represented by factorized quantum curves. In this paper, we show that this factorized description extends naturally to quantum curves associated with del Pezzo geometries possessing exceptional Weyl-group symmetries in the presence of FI parameters. We find that the vertices of the corresponding fundamental domains, identified with Voronoi polytopes of exceptional root lattices, are realized as factorized quantum curves built from canonical operators interpreted as 5-branes dressed with FI parameters. This provides a physical realization of the vertices of the Voronoi polytopes as ``extremal'' brane configurations. Current browse context: hep-th References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) IArxiv Recommender (What is IArxiv?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.