Surface Operators and Exact Holography

Non-local operators, supported on submanifolds of spacetime, often encode fascinating physical insights about a theory and can serve as order parameters for phase transitions. In this talk, we will explore various aspects of 1/2​ BPS surface operators in N=4 super Yang-Mills. Specifically, I will show how supergravity computes exactly the planar limit of certain correlation functions of surface operators, even though they receive nontrivial quantum corrections. In particular, we will compute correlation functions with Chiral Primary Operators by localizing N = 4 super Yang-Mills on S^4 to a deformed version of 2d Yang-Mills on S^2. These correlation functions, which have a finite number of quantum corrections, can also be computed perturbatively in four dimensions. I will show the exact agreement between these approaches and the corresponding supergravity result. This talk is based on 2406.08541, work in collaboration with Changha Choi and Jaume Gomis.