- The paper's main contribution is deriving a formula to extract OPE data analytically as a function of spin in conformal theories.
- It employs analytic continuation to Lorentzian signature and leverages high-energy Regge bounds to ensure convergence.
- The findings offer key insights into the suppression of higher-derivative interactions and advancements in understanding AdS/CFT dualities.
The paper "Analyticity in Spin in Conformal Theories" by Simon Caron-Huot presents a detailed analysis of the analytic properties of conformal theory correlators concerning spin. Conformal theories, which are intrinsic in high-energy physics, are distinguished by the spectrum and three-point functions of local operators. The central problem addressed in this paper is the extraction of this data as an analytic function of spin, paralleling the classical results established by Froissart and Gribov in S-matrix theory.
Caron-Huot presents a formula that extracts operator product expansion (OPE) data as an analytic function of spin, sensitive to the "imaginary part" after analytic continuation to Lorentzian signature. This paper leverages recent bounds on the high-energy Regge limit to establish convergence of the series. The derived formula is effective at extracting $1/J$ expansions at large spin, offering controlled error terms when substituting cross-channel data. The proposed methodology is significant in large-N theories, where the "imaginary part" is saturated by single-trace operators.
In establishing the phenomenon of analyticity in spin, the paper makes bold implications for Anti-de Sitter (AdS) space/local gravity dual spaces. Notably, it manifests the suppression of bulk higher-derivative interactions in theories with a sparse spectrum, which is emblematic of a gravitational dual theory in AdS. This novel insight has critical implications for effective field theories aiming to represent quantum gravity.
A substantial portion of the paper is devoted to discussing the rigorous establishment of the analytic properties. It is highlighted that in unitary conformal field theories, OPE coefficients align within rigid analytic functions rather than being independent. This finding aligns with expectations from classic dispersion relations and Regge behavior requirements in S-matrix theory. The detailed derivation furthers the understanding of how crossing symmetry and high-energy behaviors constrain operator interactions at the string level in a dual theory.
From a speculative standpoint, the implications of this research extend beyond potential interactions within quantum gravity. By using these results, large-N dual theories may offer new insights into lagrangians with suppressed higher-derivative terms, contributing to a more fine-grained understanding of quantum field theories and potentially beneficial future developments of string theory frameworks.
This paper contributes to the existing body of literature by offering not only new computational techniques for deriving operator expansions but also providing a framework for understanding the constraints imposed by analytic properties in spin. These insights and techniques can be expected to infiltrate future theoretical advancements in high energy physics, potentially enabling greater precision in numerical bootstrap methodologies and beyond.
In future explorations of analyticity in spin within conformal theories, continued development of the physical implications of these advancements suggests a promising frontier in understanding the structure of conformal field theories and their associated dualities in AdS/CFT correspondence.