Regge spectroscopy of higher twist states in $\mathcal{N}=4$ supersymmetric Yang-Mills theory

TL;DR

This paper investigates higher-twist Regge trajectories in $ 4$ supersymmetric Yang-Mills theory using the Quantum Spectral Curve, revealing new weak-coupling behavior and connecting trajectories across the Riemann surface.

Contribution

It analytically resolves degeneracies among horizontal trajectories and demonstrates the linear dependence of the Regge intercept on coupling, bridging weak and strong coupling regimes.

Findings

Regge intercept depends linearly on coupling at weak coupling

Degeneracy of non-local operators is analytically resolved

Numerical results interpolate to strong coupling

Abstract

We study a family of higher-twist Regge trajectories in $\mathcal{N}=4$ supersymmetric Yang-Mills theory using the Quantum Spectral Curve. We explore the many-sheeted Riemann surface connecting the different trajectories and show the interplay between the degenerate non-local operators known as horizontal trajectories. We resolve their degeneracy analytically by computing the first non-trivial order of the Regge intercept at weak coupling, which exhibits new behaviour: it depends linearly on the coupling. This is consistent with our numerics, which interpolate all the way to strong coupling.