2024/09/09 by Igor Mol, Mol, Igor · 1 citation
Earth and Planetary Sciences · Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #Geophysics and Gravity Measurements #High Energy Physics - Theory (hep-th) #Solar and Space Plasma Dynamics
paper · pdf · doi:10.48550/arxiv.2409.05936
openalex publication_date 2024/09/09 · openalex created_date 2024/11/01 · openalex updated_date 2026/07/28
In this note, we continue our study of Liouville theory and celestial amplitudes by deriving a set of partial differential equations governing the n-point MHV celestial amplitudes for gluons and gravitons, parametrised by the Liouville coupling constant b. These equations provide a systematic framework for computing the perturbative expansion in b of the celestial amplitudes, which are known to reproduce the tree-level MHV n-point functions for pure Yang-Mills and Einstein gravity in the semiclassical b→0 limit. We demonstrate that the O(b2) corrections are logarithmic for both gluons and gravitons. Furthermore, we compute the correction to the celestial operator product expansion (OPE) parametrised by b2. In the case of gluons, the resulting deformation of the celestial OPE is shown to be isomorphic to the one-loop correction of the celestial OPE in pure Yang-Mills theory. We then propose that "celestial Liouville theory," extended beyond the semiclassical limit, encodes the one-loop regime of pure Yang-Mills theory. A formally analogous computation is performed for Einstein gravity to ascertain the deformation of the celestial OPE induced by a non-zero Liouville coupling constant. However, as we shall explain, the physical interpretation of this result remains an open problem due to the intricate nature of the loop-corrected holomorphic collinear limit in graviton scattering amplitudes.