Approximate symmetries in d = 4 CFTs with an Einstein gravity dual

A bstract By applying the stress-tensor-scalar operator product expansion (OPE) twice, we search for algebraic structures in d = 4 conformal field theories (CFTs) with a pure Einstein gravity dual. We find that rescaled mode defined by an integral of stress tensor T ++ on 2 plane satisfies Virasoro-like algebra when dimension scalar is large. The structure enhanced to include Kac-Moody-type if incorporate −− component. In our scheme, central terms are finite. It remains challenging directly compute stress-tensor sector four-point functions at large charge, which, based holography and bootstrap methods, were recently shown have Virasoro/ $$ \mathcal{W} W -algebra vacuum block-like structure.