Rationality of the Anomalous Dimensions in N=4 SYM theory

TL;DR

This paper demonstrates that in N=4 SYM theory, all perturbative anomalous dimensions of local operators can be expressed as polynomials in their one-loop anomalous dimension, with coefficients being rational functions of N_c.

Contribution

It establishes a universal polynomial relation for anomalous dimensions in N=4 SYM, revealing a rational structure in the coefficients based on the number of colors.

Findings

Anomalous dimensions are polynomial functions of one-loop dimensions.

Coefficients of these polynomials are rational functions of N_c.

Universal structure applies to all perturbative corrections.

Abstract

We reconsider the general constraints on the perturbative anomalous dimensions in conformal invariant QFT and in particular in N=4 SYM with gauge group SU(N_c). We show that all the perturbative corrections to the anomalous dimension of a renormalized gauge invariant local operator can be written as polynomials in its one loop anomalous dimension. In the N=4 SYM theory the coefficients of these polynomials are rational functions of the number of colours N_c.