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

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 a resealed mode operator defined by an integral of the stress tensor T++ on a d = 2 plane satisfies a Virasoro-like algebra when the dimension of the scalar is large. The structure is enhanced to include a Kac-Moody-type algebra if we incorporate the T-- component. In our scheme, the central terms are finite. It remains challenging to directly compute the stress-tensor sector of d = 4 scalar four-point functions at large central charge, which, based on holography and bootstrap methods, were recently shown to have a Virasoro/W-algebra vacuum block-like structure.

Automated summary

By studying d = 4 conformal field theories with a pure Einstein gravity dual, we have discovered interesting results about algebraic structures. Under certain conditions, a rescaled mode operator satisfies a Virasoro algebra, and the structure is enhanced to a Kac-Moody algebra when additional components are incorporated.