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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/2509.08876 |
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| _version_ | 1866908531540623360 |
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| author | Bolla, Ignacio Carreño Franco, Sebastián Rodríguez-Gómez, Diego |
| author_facet | Bolla, Ignacio Carreño Franco, Sebastián Rodríguez-Gómez, Diego |
| contents | We study the Hilbert series for $5d$ Superconformal Field Theories (SCFTs) engineered by Generalized Toric Polygons (GTPs), which extend the geometric realization of these theories from toric Calabi-Yau 3-folds to theories associated to general webs of 5- and 7-branes. Smoothed T-cones provide fundamental building blocks of GTP tessellations, generalizing the role of minimal triangles in toric diagrams. Building on this construction, we propose an extension of the Martelli-Sparks-Yau algorithm for computing Hilbert series of toric Calabi-Yau 3-folds that computes the Ehrhart series directly from GTP tessellations. The Ehrhart series is an invariant under Hanany-Witten transitions, which translate geometrically into polytope mutations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08876 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Hilbert Series for Generalized Toric Polygons Bolla, Ignacio Carreño Franco, Sebastián Rodríguez-Gómez, Diego High Energy Physics - Theory We study the Hilbert series for $5d$ Superconformal Field Theories (SCFTs) engineered by Generalized Toric Polygons (GTPs), which extend the geometric realization of these theories from toric Calabi-Yau 3-folds to theories associated to general webs of 5- and 7-branes. Smoothed T-cones provide fundamental building blocks of GTP tessellations, generalizing the role of minimal triangles in toric diagrams. Building on this construction, we propose an extension of the Martelli-Sparks-Yau algorithm for computing Hilbert series of toric Calabi-Yau 3-folds that computes the Ehrhart series directly from GTP tessellations. The Ehrhart series is an invariant under Hanany-Witten transitions, which translate geometrically into polytope mutations. |
| title | A Hilbert Series for Generalized Toric Polygons |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.08876 |