Symmetries of the Celestial Supersphere
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918092239536128 |
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| author | Tropper, Adam |
| author_facet | Tropper, Adam |
| contents | We study the celestial CFT dual to theories with bulk supersymmetry. The boundary theory realizes supersymmetry in the spirit of the Green-Schwarz superstring: there is manifest 4d super-Poincaré symmetry, but no 2d superconformal symmetry. Nevertheless, we can extend the celestial sphere itself to a supermanifold -- the celestial supersphere. This provides a unified framework for describing key features of celestial holography, including conformally soft theorems, OPEs, and chiral soft algebras. Using these tools, we demonstrate that the $\frak{bms}_{4}$ algebra extends to a novel $\frak{sbms}_{4|\mathcal{N}}$ algebra. We also relate the supersymmetric $L(w_{1+\infty}^\wedge)$ algebra to Hamiltonian vector fields on $\mathbb{C}^{2|\mathcal{N}}$, consistent with the expectation from twistor theory, and deduce the deformation of this algebra by a cosmological constant, $Λ$. These results are all universal and independent of the specific details of the underlying theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_13113 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetries of the Celestial Supersphere Tropper, Adam High Energy Physics - Theory We study the celestial CFT dual to theories with bulk supersymmetry. The boundary theory realizes supersymmetry in the spirit of the Green-Schwarz superstring: there is manifest 4d super-Poincaré symmetry, but no 2d superconformal symmetry. Nevertheless, we can extend the celestial sphere itself to a supermanifold -- the celestial supersphere. This provides a unified framework for describing key features of celestial holography, including conformally soft theorems, OPEs, and chiral soft algebras. Using these tools, we demonstrate that the $\frak{bms}_{4}$ algebra extends to a novel $\frak{sbms}_{4|\mathcal{N}}$ algebra. We also relate the supersymmetric $L(w_{1+\infty}^\wedge)$ algebra to Hamiltonian vector fields on $\mathbb{C}^{2|\mathcal{N}}$, consistent with the expectation from twistor theory, and deduce the deformation of this algebra by a cosmological constant, $Λ$. These results are all universal and independent of the specific details of the underlying theory. |
| title | Symmetries of the Celestial Supersphere |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.13113 |