Towards the $\beta$ function of SU(2) with adjoint matter using Pauli-Villars fields

TL;DR

This paper investigates the beta function of SU(2) gauge theories with adjoint matter using gradient flow, exploring phase diagrams and lattice simulations to understand their conformal or confining nature.

Contribution

It presents the first steps in computing the beta function of SU(2) theories with adjoint matter via gradient flow, including phase diagram analysis and lattice ensemble generation.

Findings

Explored phase diagram with Wilson fermions and Pauli-Villars fields.

Generated ensembles at multiple lattice volumes and spacings.

Tuned fermion mass near the chiral limit for analysis.

Abstract

The family of SU(2) theories with matter transforming in the adjoint representation has attracted interest from many angles. The two-flavour theory, known as Minimal Walking Technicolor, has a body of evidence pointing to it being in the conformal window with anomalous dimension $\gamma_{*}\approx0.3$. Perturbative calculations would suggest that the one-flavour theory should be confining and chirally broken; however, lattice studies of the theory have been inconclusive. In this contribution we present a first look at efforts towards the computation of the beta function of these theories using the gradient flow methodology. Following an exploration of the phase diagram of the two theories with Wilson fermions and additional Pauli-Villars fields, we tune the bare fermion mass to near the chiral limit, and subsequently generate ensembles at five lattice volumes and a range of lattice spacings.