Light and Shadow OPEs: A Carroll Symmetric Approach to Flat Holography

In this work, we fix the leading term in the operator algebra of light-transformed operators in the context of flat space holography. Starting with light-transformed graviton correlators, we show that the OPE obtained by taking the collinear limit satisfies translation symmetry at the leading order not independently but with assistance from the sub-leading order. Motivated by this result, we start with a general CFT-like ansatz for the OPE and, by keeping track of the sub-leading term, derive an expression for the scaling dimension of the operator appearing in the leading term. We further show that we can fix the OPE coefficient corresponding to this term as well. We use this result to find the OPE for well-studied theories like gravity, Yang-Mills and Einstein-Yang-Mills theory, and find that the scaling dimension found from our formula matches with the one obtained by looking at the collinear limit of bulk momentum space vertices. We initiate a similar study for operators in the shadow basis by looking at the OPE of shadow-transformed graviton correlators.