BCFT One-point Functions of Coulomb Branch Operators
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866911174023446528 |
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| author | Bason, Davide Di Pietro, Lorenzo Valandro, Roberto van Muiden, Jesse |
| author_facet | Bason, Davide Di Pietro, Lorenzo Valandro, Roberto van Muiden, Jesse |
| contents | We show that supersymmetry can be used to compute the BCFT one-point function coefficients for chiral primary operators, in 4d $\mathcal{N}=2$ SCFTs with $\frac{1}{2}$-BPS boundary conditions. The main ingredient is the hemisphere partition function, with the boundary condition on the equatorial $S^3$. A supersymmetric Ward identity relates derivatives with respect to the chiral coupling constants to the insertion of the primaries at the pole of the hemisphere. Exact results for the one-point functions can be then obtained in terms of the localization matrix model. We discuss in detail the example of the super Maxwell theory in the bulk, interacting with 3d $\mathcal{N}=2$ SCFTs on the boundary. In particular we derive the action of the SL(2,$\mathbb{Z}$) duality on the one-point functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_17888 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | BCFT One-point Functions of Coulomb Branch Operators Bason, Davide Di Pietro, Lorenzo Valandro, Roberto van Muiden, Jesse High Energy Physics - Theory We show that supersymmetry can be used to compute the BCFT one-point function coefficients for chiral primary operators, in 4d $\mathcal{N}=2$ SCFTs with $\frac{1}{2}$-BPS boundary conditions. The main ingredient is the hemisphere partition function, with the boundary condition on the equatorial $S^3$. A supersymmetric Ward identity relates derivatives with respect to the chiral coupling constants to the insertion of the primaries at the pole of the hemisphere. Exact results for the one-point functions can be then obtained in terms of the localization matrix model. We discuss in detail the example of the super Maxwell theory in the bulk, interacting with 3d $\mathcal{N}=2$ SCFTs on the boundary. In particular we derive the action of the SL(2,$\mathbb{Z}$) duality on the one-point functions. |
| title | BCFT One-point Functions of Coulomb Branch Operators |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2311.17888 |