Orthogonality of Q-Functions up to Wrapping in Planar N=4 Super Yang-Mills Theory

TL;DR

This paper establishes orthogonality relations for Q-functions in the sl(2) sector of planar N=4 super Yang-Mills theory, providing universal measures that vanish at all orders before wrapping corrections.

Contribution

It introduces simple universal measures for Q-functions that ensure orthogonality across different spins, relaxing previous assumptions in the Separation of Variables framework.

Findings

Q-functions of operators with different spins vanish at all perturbative orders

Universal measures are constructed to achieve orthogonality

Results may guide extensions to other sectors and integrable models

Abstract

We construct orthogonality relations in the Separation of Variables framework for the sl(2) sector of planar N=4 supersymmetric Yang-Mills theory. Specifically, we find simple universal measures that make Q-functions of operators with different spins vanish at all orders in perturbation theory, prior to wrapping corrections. To analyze this rank-one sector, we relax some of the assumptions thus far considered in the Separation of Variables framework. Our findings may serve as guidelines for extending this formalism to other sectors of the theory as well as other integrable models