Complex Spin: The Missing Zeroes and Newton's Dark Magic

TL;DR

This paper explores the analytic continuation of conformal field theory data for complex spin in N=4 SYM, revealing zeroes in structure constants that lead to operator decoupling, using Newton's interpolation series.

Contribution

It introduces a physical picture of operator organization in complex spin and applies Newton's interpolation to analyze the analytic structure of CFT data.

Findings

Operators form analytic families with zeroes in structure constants at certain spins

Zeroes cause decoupling of operator families in the complex spin plane

Newton's interpolation series effectively explores the complex spin half-plane

Abstract

Conformal Regge theory predicts the existence of analytically continued CFT data for complex spin. How could this work when there are so many more operators with large spin compared to small spin? Using planar N=4 SYM as a testground we find a simple physical picture. Operators do organize themselves into analytic families but the continuation of the higher families have zeroes in their structure OPE constants for lower integer spins. They thus decouple. Newton's interpolation series technique is perfectly suited to this physical problem and will allow us to explore the right complex spin half-plane.