Long-range SL(2) Baxter equation in N=4 super-Yang-Mills theory

TL;DR

The paper proposes an all-loop generalization of the SL(2) Baxter equation for N=4 SYM in the asymptotic, wrapping-free regime, using deformed dressing factors and a Q-operator formalism to encode the spectrum of twist-L operators. It develops an asymptotic large-spin expansion to derive a cusp-equation for the universal cusp anomalous dimension Γ_cusp(g), and provides a perturbative weak-coupling solution with explicit coefficients that reproduce known multi-loop results while revealing an iterative structure. A key contribution is linking conformal spin renormalization to the anomalous dimensions through integral representations of the dressing factors and the Q-function. The work also discusses limitations due to wrapping effects and highlights ongoing debates in the four-loop regime, signaling directions for refining the framework and extending it to all sectors.

Abstract

Relying on a few lowest order perturbative calculations of anomalous dimensions of gauge invariant operators built from holomorphic scalar fields and an arbitrary number of covariant derivatives in maximally supersymmetric gauge theory, we propose an all-loop generalization of the Baxter equation which determines their spectrum. The equation does not take into account wrapping effects and is thus asymptotic in character. We develop an asymptotic expansion of the deformed Baxter equation for large values of the conformal spin and derive an integral equation for the cusp anomalous dimension.