From N=4 gauge theory to N=2 conformal QCD: three-loop mixing of scalar composite operators

TL;DR

This paper computes the three-loop planar dilatation operator for scalar operators in an N=2 superconformal gauge theory, revealing special contributions at the orbifold point and insights into the nature of excitations and integrability.

Contribution

It derives the three-loop dilatation operator in an N=2 superconformal theory and explores its behavior across a coupling ratio, connecting orbifold and QCD limits.

Findings

zeta(3) terms vanish at the orbifold point

Imaginary parts in scalar excitation dispersion relations

Elementary excitations likely fermions and derivatives

Abstract

We derive the planar dilatation operator in the closed subsector of scalar composite operators of an N=2 superconformal quiver gauge theory to three loops. By tuning the ratio of its two gauge couplings we interpolate between a Z_2 orbifold of N=4 SYM theory and N=2 superconformal QCD. We find zeta(3) contributions at three loops that disappear when the theory is at the orbifold point. They are responsible for imaginary contributions to the dispersion relation of a single scalar excitation in the spin-chain picture. This points towards an interpretation of the individual scalar excitations as effective rather than as elementary magnons. We argue that the elementary excitations should be associated with certain fermions and covariant derivatives, and that integrability in the respective subsectors should persist at least to two loops.