Charting the Triality Webs for All Smooth Fano 3-Folds

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Auteurs principaux:	Carcamo, Mario, Franco, Sebastián
Format:	Preprint
Publié:	2025
Sujets:	High Energy Physics - Theory
Accès en ligne:	Acceder al recurso
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_version_	1866908310911844352
author	Carcamo, Mario Franco, Sebastián
author_facet	Carcamo, Mario Franco, Sebastián
contents	We determine all toric phases for the $2d$ $(0,2)$ theories on D1-branes probing the complex cones over the 18 smooth Fano 3-folds, whose toric diagrams correspond to the regular reflexive polytopes in 3 dimensions. These results significantly expand the list of explicitly known gauge theories on D1-branes over toric CY 4-folds. We go beyond the classification of toric phases and map the corresponding triality webs, establishing how the toric phases are connected by triality. The size and complexity of the webs constructed in this work far surpass any previously known examples, both in the contexts of Calabi-Yau 3-folds and 4-folds-with several of these CY 4-folds exhibiting hundreds of toric phases. We propose various new approaches for characterizing triality webs. Our work lays the foundation for a comprehensive exploration of the structure of triality webs.
format	Preprint
id	arxiv_https___arxiv_org_abs_2504_01088
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Charting the Triality Webs for All Smooth Fano 3-Folds Carcamo, Mario Franco, Sebastián High Energy Physics - Theory We determine all toric phases for the $2d$ $(0,2)$ theories on D1-branes probing the complex cones over the 18 smooth Fano 3-folds, whose toric diagrams correspond to the regular reflexive polytopes in 3 dimensions. These results significantly expand the list of explicitly known gauge theories on D1-branes over toric CY 4-folds. We go beyond the classification of toric phases and map the corresponding triality webs, establishing how the toric phases are connected by triality. The size and complexity of the webs constructed in this work far surpass any previously known examples, both in the contexts of Calabi-Yau 3-folds and 4-folds-with several of these CY 4-folds exhibiting hundreds of toric phases. We propose various new approaches for characterizing triality webs. Our work lays the foundation for a comprehensive exploration of the structure of triality webs.
title	Charting the Triality Webs for All Smooth Fano 3-Folds
topic	High Energy Physics - Theory
url	https://arxiv.org/abs/2504.01088

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