Three-Point Functions in N=4 SYM Theory at One-Loop

TL;DR

This paper investigates one-loop corrections to three-point functions in N=4 SYM, revealing scheme-dependent contributions and establishing a connection between conformal field theory and integrable spin chains, suggesting integrability at this loop order.

Contribution

It demonstrates the scheme dependence of one-loop corrections and links these corrections to integrable spin chain models, highlighting integrability in planar N=4 SYM at one-loop.

Findings

Explicit one-loop correction expressions linked to spin chain Hamiltonians

Scheme dependence of contributing Feynman diagrams

Connection between planar CFT and string field theory structures

Abstract

We analyze the one-loop correction to the three-point function coefficient of scalar primary operators in N=4 SYM theory. By applying constraints from the superconformal symmetry, we demonstrate that the type of Feynman diagrams that contribute depends on the choice of renormalization scheme. In the planar limit, explicit expressions for the correction are interpreted in terms of the hamiltonians of the associated integrable closed and open spin chains. This suggests that at least at one-loop, the planar conformal field theory is integrable with the anomalous dimensions and OPE coefficients both obtainable from integrable spin chain calculations. We also connect the planar results with similar structures found in closed string field theory.