Non-toric brane webs, Calabi-Yau 3-folds, and 5d SCFTs
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909803267227648 |
|---|---|
| author | Alexeev, Valery Argüz, Hülya Bousseau, Pierrick |
| author_facet | Alexeev, Valery Argüz, Hülya Bousseau, Pierrick |
| contents | We study webs of 5-branes with 7-branes in Type IIB string theory from a geometric perspective. Mathematically, a web of 5-branes with 7-branes is a tropical curve in $\mathbb{R}^2$ with focus-focus singularities introduced. To any such a web $W$, we attach a log Calabi-Yau surface $(Y,D)$ with a line bundle $L$. We then describe supersymmetric webs, which are webs defining 5d superconformal field theories (SCFTs), in terms of the geometry of $(Y,D,L)$. We also introduce particular supersymmetric webs called ``consistent webs", and show that any 5d SCFT defined by a supersymmetric web can be obtained from a consistent web by adding free hypermultiplets. Using birational geometry of degenerations of log Calabi-Yau surfaces, we provide an algorithm to test the consistency of a web in terms of its dual polygon. Moreover, for a consistent web $W$, we provide an algebro-geometric construction of the mirror $\mathcal{X}^{\mathrm{can}}$ to $(Y,D,L)$, as a non-toric canonical 3-fold singularity, and show that M-theory on $\mathcal{X}^{\mathrm{can}}$ engineers the same 5d SCFT as $W$. We also explain how to derive explicit equations for $\mathcal{X}^{\mathrm{can}}$ using scattering diagrams, encoding disk worldsheet instantons in the A-model, or equivalently the BPS states of an auxiliary rank one 4d $\mathcal{N}=2$ theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04714 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-toric brane webs, Calabi-Yau 3-folds, and 5d SCFTs Alexeev, Valery Argüz, Hülya Bousseau, Pierrick High Energy Physics - Theory Algebraic Geometry Symplectic Geometry We study webs of 5-branes with 7-branes in Type IIB string theory from a geometric perspective. Mathematically, a web of 5-branes with 7-branes is a tropical curve in $\mathbb{R}^2$ with focus-focus singularities introduced. To any such a web $W$, we attach a log Calabi-Yau surface $(Y,D)$ with a line bundle $L$. We then describe supersymmetric webs, which are webs defining 5d superconformal field theories (SCFTs), in terms of the geometry of $(Y,D,L)$. We also introduce particular supersymmetric webs called ``consistent webs", and show that any 5d SCFT defined by a supersymmetric web can be obtained from a consistent web by adding free hypermultiplets. Using birational geometry of degenerations of log Calabi-Yau surfaces, we provide an algorithm to test the consistency of a web in terms of its dual polygon. Moreover, for a consistent web $W$, we provide an algebro-geometric construction of the mirror $\mathcal{X}^{\mathrm{can}}$ to $(Y,D,L)$, as a non-toric canonical 3-fold singularity, and show that M-theory on $\mathcal{X}^{\mathrm{can}}$ engineers the same 5d SCFT as $W$. We also explain how to derive explicit equations for $\mathcal{X}^{\mathrm{can}}$ using scattering diagrams, encoding disk worldsheet instantons in the A-model, or equivalently the BPS states of an auxiliary rank one 4d $\mathcal{N}=2$ theory. |
| title | Non-toric brane webs, Calabi-Yau 3-folds, and 5d SCFTs |
| topic | High Energy Physics - Theory Algebraic Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2410.04714 |