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

Abstract

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 rescaled 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/$$ \mathcal{W} $$ W -algebra vacuum block-like structure.

Thermal stress tensor correlators, OPE and holography

“…[22][23][24][25]) but at the moment the full resummed correlator in d > 2 is only known in the ∆L→∞ limit [26]. (see [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] for related work). 4 In particular, it has been observed in the d = 2 case that thermalization of multi stress-tensor operators happens only to leading order in the 1/CT expansion (see [45][46][47] for recent discussions).…”

Averaged null energy and the renormalization group

“…Their OPEs and crossing relations have been studied in [3,14,[58][59][60][61]. Light-ray operators built from the stress tensor have special algebraic properties [12,32,[62][63][64][65][66][67][68] and encode some universal features of higher-dimensional CFT [69][70][71][72]. They have been studied perturbatively in specific examples [73][74][75].…”