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.
Highlights
An operator product expansion (OPE) is one of the most fundamental postulates in local quantum field theories [1, 2]
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
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
Summary
An operator product expansion (OPE) is one of the most fundamental postulates in local quantum field theories [1, 2]. Our derivation closely follows the relevant works [19, 20] where similar results were obtained in a slightly different way These works started with a pair of timelike-separated operators, took the Regge-like limit of the timelike OPE block B∆♦,J proposed by [15, 16], which differs from the spacelike OPE block B∆,J of [18] we use in this paper, and analytically continued the result to the spacelike configuration. The emergence of light-ray operators in the Regge limit was envisaged already in [14, 21], where the Regge limit of a pair of spacelike-separated operators in a Minkowski patch is interpreted as the ordinary OPE limit of a pair of timelike-separated operators associated to the original pair in a different Minkowski patch with a light-ray operator exchanged in the timelike OPE channel The rest of the appendices contain some technical details skipped in the main text
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