Multitwist Trajectories and Decoupling Zeros in Conformal Field Theory

Area of Science:

• Theoretical physics
• High-energy physics
• Quantum field theory

Background:

• Conformal Regge theory predicts analytic continuation of conformal field theory data for complex spin.
• The organization of operators with large versus small spin presents a challenge to this prediction.

Purpose of the Study:

• To investigate the physical mechanism behind analytically continued conformal field theory data for complex spin.
• To utilize planar N=4 Super Yang-Mills (SYM) theory as a testing ground for these theoretical predictions.

Main Methods:

• Analysis of operator organization in analytic families.
• Examination of structure operator product expansion (OPE) constants for higher families at lower integer spins.
• Application of Newton's interpolation series technique.

Main Results:

• Operators organize into analytic families.
• Higher families exhibit zeros in their structure OPE constants for lower integer spins, causing them to decouple.
• Newton's interpolation series is well-suited for exploring the complex spin half-plane.

Conclusions:

• A simple physical picture explains the analytic continuation of conformal field theory data for complex spin.
• Decoupling of higher families at lower spins resolves the apparent contradiction.
• Newton's interpolation series provides a powerful tool for future investigations in this area.