Regge OPE blocks and light-ray operators

Abstract

We consider the structure of the operator product expansion (OPE) in conformal field theory by employing the OPE block formalism. The OPE block acted on the vacuum is promoted to an operator and its implications are examined on a non-vacuum state. We demonstrate that the OPE block is dominated by a light-ray operator in the Regge limit, which reproduces precisely the Regge behavior of conformal blocks when used inside scalar four-point functions. Motivated by this observation, we propose a new form of the OPE block, called the light-ray channel OPE block that has a well-behaved expansion dominated by a light-ray operator in the Regge limit. We also show that the two OPE blocks have the same asymptotic form in the Regge limit and confirm the assertion that the Regge limit of a pair of spacelike-separated operators in a Minkowski patch is equivalent to the OPE limit of a pair of timelike-separated operators associated with the original pair in a different Minkowski patch.

Regge conformal blocks from the Rindler-AdS black hole and the pole-skipping phenomena

“…It would be important to consider the general configurations of the boundary points. In the bulk with Lorentzian signature, the domain of integration for the gravity duals of conformal blocks depends on the causal structure of the boundary points [28,34,64,65]. Therefore, the domain of integration for the general configurations may be more complicated than the one in our case.…”

“…• In our construction, we use the Kruskal coordinates U and V . On the other hand, light-cone coordinates in the Poincaré patch are used for the construction of the Regge OPE blocks in [22,28].…”

Regge conformal blocks from the Rindler-AdS black hole and the pole-skipping phenomena

“…It would be important to consider the general configurations of the boundary points. In the bulk with Lorentzian signature, the domain of integration for the gravity duals of conformal blocks depends on the causal structure of the boundary points [29,35,65,66]. Therefore, the domain of integration for the general configurations may be more complicated than the one in our case.…”

“…• In our construction, we use the Kruskal coordinates U and V . On the other hand, light-cone coordinates in the Poincaré patch are used for the construction of the Regge OPE blocks in [23,29].…”

“…See subsection 3.5 for the examples with = 1 and = 2 5. See a connection between the Gegenbauer polynomials and two-point functions with the projectors in[29,39] 6. For example, a spin-2 symmetric field can be decomposed into a spin-2 symmetric traceless part and a scalar part.…”