Spacetime $Lw_{1+\infty}$ Symmetry and Self-Dual Gravity in Plebanski Gauge
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| Format: | Preprint |
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2025
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| _version_ | 1866913787234222080 |
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| author | Miller, Noah |
| author_facet | Miller, Noah |
| contents | The space of self-dual Einstein spacetimes in 4 dimensions is acted on by an infinite dimensional Lie algebra called the $Lw_{1+\infty}$ algebra. In this work we explain how one can ``build up'' self-dual metrics by acting on the flat metric with an arbitrary number of infinitesimal $Lw_{1+\infty}$ transformations, using a convenient choice of gauge called Plebanski gauge. We accomplish this through the use of something called a ``perturbiner expansion,'' which will perturbatively generate for us a self-dual metric starting from an initial set of quasinormal modes called integer modes. Each integer mode corresponds to a particular $Lw_{1+\infty}$ transformation, and this perturbiner expansion of integer modes will be written as a sum over ``marked tree graphs,'' instead of momentum space Feynman diagrams.
We find that a subset of the $Lw_{1+\infty}$ transformations act as spacetime diffeomorphisms, and the algebra of these diffeomorphisms is $w_{\infty} \ltimes f$. We also show all analogous results hold for the $Ls$ algebra in self-dual Yang Mills. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_07176 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spacetime $Lw_{1+\infty}$ Symmetry and Self-Dual Gravity in Plebanski Gauge Miller, Noah High Energy Physics - Theory The space of self-dual Einstein spacetimes in 4 dimensions is acted on by an infinite dimensional Lie algebra called the $Lw_{1+\infty}$ algebra. In this work we explain how one can ``build up'' self-dual metrics by acting on the flat metric with an arbitrary number of infinitesimal $Lw_{1+\infty}$ transformations, using a convenient choice of gauge called Plebanski gauge. We accomplish this through the use of something called a ``perturbiner expansion,'' which will perturbatively generate for us a self-dual metric starting from an initial set of quasinormal modes called integer modes. Each integer mode corresponds to a particular $Lw_{1+\infty}$ transformation, and this perturbiner expansion of integer modes will be written as a sum over ``marked tree graphs,'' instead of momentum space Feynman diagrams. We find that a subset of the $Lw_{1+\infty}$ transformations act as spacetime diffeomorphisms, and the algebra of these diffeomorphisms is $w_{\infty} \ltimes f$. We also show all analogous results hold for the $Ls$ algebra in self-dual Yang Mills. |
| title | Spacetime $Lw_{1+\infty}$ Symmetry and Self-Dual Gravity in Plebanski Gauge |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2504.07176 |