Multitwist Trajectories and Decoupling Zeros in Conformal Field Theory

Abstract

Conformal Regge theory predicts the existence of analytically continued conformal field theory 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 test ground, we find a simple physical picture. Operators do organize themselves into analytic families but the continuation of the higher families have zeros in their structure operator product expansion 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 complex spin half-plane. Published by the American Physical Society 2025