IAS Physics Group Meeting

Abstract: Quantum self-dual gravity is a one-loop-exact, UV and IR finite, diffeomorphism invariant, non-unitary theory of quantum gravity in 4-dimensions. In lightcone gauge, the theory can be formulated in terms of a simple ghost-free cubic action. The only non-zero scattering amplitudes in this theory are the one-loop-all-plus amplitudes which match those of pure Einstein gravity. In some sense, the theory's only role in life is to compute the one-loop-all-plus Einstein gravity amplitudes, which are finite and rational, but it can also be thought of as a self-contained theory in its own right.

Despite the simplicity of the theory, it in many ways remains quite mysterious. For instance nobody has yet calculated all of the amplitudes in this theory (although there is a conjectured formula dating back to 1998 by Bern, Dixon, Perelstein, and Rosowsky that has been checked up to 6-pts).

Tantalizingly, the only singularities of the one-loop-all-plus amplitudes are holomorphic collinear singularities which take the form of Lw_1+infinity OPEs. These OPEs are already known to generate the classical solutions of theory and the MHV amplitudes, and one cannot help but wonder if the Lw_1+infinity OPEs can be used to fully solve the theory at loop-level.

This talk will discuss these ideas from an ongoing work with Alfredo Guevara and Elizabeth Himwich.

Based on:
https://arxiv.org/abs/2506.05460
https://arxiv.org/abs/2504.07176