I will report on work to appear shortly with my student, Victor Fernandez. The celestial chiral algebras of “twistorial” theories, 4d theories with local holomorphic lifts to twistor space, are associative even at the quantum level. In this work, we use elementary considerations, such as symmetries and associativity, to find closed-form expressions for all coefficients (i.e., at arbitrary loop order) of the OPEs for the celestial chiral algebras associated to twistorial theories, in particular self-dual Yang-Mills theory coupled to special choices of matter; similar considerations apply also for self-dual general relativity coupled to a special matter sector. This work constitutes a preliminary step in a program proposed by Costello and myself called the chiral algebra bootstrap, in which correlation functions for such chiral algebras can be used to compute higher loop form factors in non-supersymmetric 4d quantum field theories.
A talk within the Pacific Northwest Particle Theory Seminar.