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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2410.16767 |
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| _version_ | 1866914983604912128 |
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| author | Moleti, Marina Valandro, Roberto |
| author_facet | Moleti, Marina Valandro, Roberto |
| contents | We study families of deformed ADE surfaces by probing them with a D2-brane in Type IIA string theory. The geometry of the total space $X$ of such a family can be encoded in a scalar field $Φ$, which lives in the corresponding ADE algebra and depends on the deformation parameters. The superpotential of the probe three dimensional (3d) theory incorporates a term that depends on the field $Φ$. By varying the parameters on which $Φ$ depends, one generates a family of 3d theories whose moduli space always includes a geometric branch, isomorphic to the deformed surface. By fibering this geometric branch over the parameter space, the total space $X$ of the family of ADE surfaces is reconstructed. We explore various cases, including when $X$ is the universal flop of length $\ell=1,2$. The effective theory, obtained after the introduction of $Φ$, provides valuable insights into the geometric features of $X$, such as the loci in parameter space where the fiber becomes singular and, more notably, the conditions under which this induces a singularity in the total space. By analyzing the monopole operators in the 3d theory, we determine the charges of certain M2-brane states arising in M-theory compactifications on $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16767 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal flops of length 1 and 2 from D2-branes at surface singularities Moleti, Marina Valandro, Roberto High Energy Physics - Theory Algebraic Geometry We study families of deformed ADE surfaces by probing them with a D2-brane in Type IIA string theory. The geometry of the total space $X$ of such a family can be encoded in a scalar field $Φ$, which lives in the corresponding ADE algebra and depends on the deformation parameters. The superpotential of the probe three dimensional (3d) theory incorporates a term that depends on the field $Φ$. By varying the parameters on which $Φ$ depends, one generates a family of 3d theories whose moduli space always includes a geometric branch, isomorphic to the deformed surface. By fibering this geometric branch over the parameter space, the total space $X$ of the family of ADE surfaces is reconstructed. We explore various cases, including when $X$ is the universal flop of length $\ell=1,2$. The effective theory, obtained after the introduction of $Φ$, provides valuable insights into the geometric features of $X$, such as the loci in parameter space where the fiber becomes singular and, more notably, the conditions under which this induces a singularity in the total space. By analyzing the monopole operators in the 3d theory, we determine the charges of certain M2-brane states arising in M-theory compactifications on $X$. |
| title | Universal flops of length 1 and 2 from D2-branes at surface singularities |
| topic | High Energy Physics - Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2410.16767 |