Near the sill of the conformal window: gauge theories with fermions in two-index representations

TL;DR

This study investigates gauge theories with fermions in two-index representations near the conformal window, using Schroedinger functional methods to analyze their beta functions and anomalous dimensions.

Contribution

It provides new lattice-based insights into the infrared behavior of SU(3) and SU(4) gauge theories with two-index fermions near the conformal window, highlighting potential walking dynamics.

Findings

SU(3) theory shows a small beta function at strong coupling.

SU(4) theory exhibits signs of walking behavior.

Mass anomalous dimension remains small even at strong coupling.

Abstract

We apply Schroedinger functional methods to two gauge theories with fermions in two-index representations: the SU(3) theory with Nf=2 adjoint fermions, and the SU(4) theory with Nf=6 fermions in the two-index antisymmetric representation. Each theory is believed to lie near the bottom of the conformal window for its respective representation. In the SU(3) theory we find a small beta function in strong coupling but we cannot confirm or rule out an infrared fixed point. In the SU(4) theory we find a hint of walking - a beta function that approaches the axis and then turns away from it. In both theories the mass anomalous dimension remains small even at the strongest couplings, much like the theories with fermions in the two-index symmetric representation investigated earlier.