2025/04/09 by Miller, Noah
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2504.07176
The space of self-dual Einstein spacetimes in 4 dimensions is acted on by an infinite dimensional Lie algebra called the Lw1+∞ 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 Lw1+∞ 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 Lw1+∞ 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 Lw1+∞ transformations act as spacetime diffeomorphisms, and the algebra of these diffeomorphisms is w∞ \ltimes f. We also show all analogous results hold for the Ls algebra in self-dual Yang Mills.