2d Sigma Models on Non-compact Calabi-Yau and ${\mathcal N}=2$ Liouville Theory
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| Format: | Preprint |
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2023
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| _version_ | 1866908360927870976 |
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| author | Gavrylenko, Pavlo Ievlev, Evgenii Marshakov, Andrei Monastyrskii, Ilia Yung, Alexei |
| author_facet | Gavrylenko, Pavlo Ievlev, Evgenii Marshakov, Andrei Monastyrskii, Ilia Yung, Alexei |
| contents | We consider a class of two dimensional conformal ${\mathcal N}=2$ supersymmetric $U(1)$ gauge linear sigma models with $N$ fields of charges $+1$ and $N$ fields of charges $-1$, whose Higgs branches are non-compact toric Calabi-Yau manifolds of complex dimension $2N-1$. We show, starting from large-$N$ approximation, that the Coulomb branch of these models, which opens up at strong coupling, is described by ${\mathcal N}=2$ Liouville theory and then extrapolate it to exact equivalence demanding the central charge of the Liouville theory to be $\hat{c}=2N-1$. Next we concentrate on mostly physically attractive $N=2$ and $N \geq 3$ cases and find there a perfect agreement of the set of complex moduli on the Calabi-Yau side with the marginal deformations in ${\mathcal N}=2$ Liouville theory, supporting proposed exact equivalence. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_02929 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | 2d Sigma Models on Non-compact Calabi-Yau and ${\mathcal N}=2$ Liouville Theory Gavrylenko, Pavlo Ievlev, Evgenii Marshakov, Andrei Monastyrskii, Ilia Yung, Alexei High Energy Physics - Theory Mathematical Physics We consider a class of two dimensional conformal ${\mathcal N}=2$ supersymmetric $U(1)$ gauge linear sigma models with $N$ fields of charges $+1$ and $N$ fields of charges $-1$, whose Higgs branches are non-compact toric Calabi-Yau manifolds of complex dimension $2N-1$. We show, starting from large-$N$ approximation, that the Coulomb branch of these models, which opens up at strong coupling, is described by ${\mathcal N}=2$ Liouville theory and then extrapolate it to exact equivalence demanding the central charge of the Liouville theory to be $\hat{c}=2N-1$. Next we concentrate on mostly physically attractive $N=2$ and $N \geq 3$ cases and find there a perfect agreement of the set of complex moduli on the Calabi-Yau side with the marginal deformations in ${\mathcal N}=2$ Liouville theory, supporting proposed exact equivalence. |
| title | 2d Sigma Models on Non-compact Calabi-Yau and ${\mathcal N}=2$ Liouville Theory |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2307.02929 |