Soft Algebras in AdS$_4$ from Light Ray Operators in CFT$_3$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910106596147200 |
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| author | Sheta, Ahmed Strominger, Andrew Tropper, Adam Wei, Hongji |
| author_facet | Sheta, Ahmed Strominger, Andrew Tropper, Adam Wei, Hongji |
| contents | Flat Minkowski space (M$^4$) and AdS$_4$ can both be conformally mapped to the Einstein cylinder. The maps may be judiciously chosen so that some null generators of the $\mathcal{I}^+$ boundary of M$^4$ coincide with antipodally-terminating null geodesic segments on the boundary of AdS$_4$. Conformally invariant nonabelian gauge theories in M$^4$ have an asymptotic $S$-algebra generated by a tower of soft gluons given by weighted null line integrals on $\mathcal{I}^+$. We show that, under the conformal map to AdS$_4$, the leading soft gluons are dual to light transforms of the conserved global symmetry currents in the boundary CFT$_3$. The tower of light ray operators obtained from the $SO(3,2)$ descendants of this light transform realize a full set of generators of the $S$-algebra in the boundary CFT$_3$. This provides a direct connection between holographic symmetry algebras in M$^4$ and AdS$_4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00096 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Soft Algebras in AdS$_4$ from Light Ray Operators in CFT$_3$ Sheta, Ahmed Strominger, Andrew Tropper, Adam Wei, Hongji High Energy Physics - Theory General Relativity and Quantum Cosmology Flat Minkowski space (M$^4$) and AdS$_4$ can both be conformally mapped to the Einstein cylinder. The maps may be judiciously chosen so that some null generators of the $\mathcal{I}^+$ boundary of M$^4$ coincide with antipodally-terminating null geodesic segments on the boundary of AdS$_4$. Conformally invariant nonabelian gauge theories in M$^4$ have an asymptotic $S$-algebra generated by a tower of soft gluons given by weighted null line integrals on $\mathcal{I}^+$. We show that, under the conformal map to AdS$_4$, the leading soft gluons are dual to light transforms of the conserved global symmetry currents in the boundary CFT$_3$. The tower of light ray operators obtained from the $SO(3,2)$ descendants of this light transform realize a full set of generators of the $S$-algebra in the boundary CFT$_3$. This provides a direct connection between holographic symmetry algebras in M$^4$ and AdS$_4$. |
| title | Soft Algebras in AdS$_4$ from Light Ray Operators in CFT$_3$ |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2601.00096 |