SU(2) gauge theory with one and two adjoint fermions towards the continuum limit

TL;DR

This study investigates the infrared properties of SU(2) gauge theories with one and two adjoint fermions, using lattice simulations to determine their mass spectra and anomalous dimensions, suggesting conformal behavior.

Contribution

It provides a detailed lattice analysis of the continuum limit for both theories, improving methods for mode number analysis and characterizing their conformal nature.

Findings

Anomalous dimension for Nf=1 approaches 0.170(6) in the continuum limit.

Anomalous dimension for Nf=2 converges to 0.291(9) with finer lattice spacing.

Infrared behavior is incompatible with chiral symmetry breaking.

Abstract

We provide an extended lattice study of the SU(2) gauge theory coupled to one Dirac fermion flavour ($N_{\mathrm{f}} =1$) transforming in the adjoint representation as the continuum limit is approached. This investigation is supplemented by numerical results obtained for the SU(2) gauge theory with two Dirac fermion flavours ($N_{\mathrm{f}} =2$) transforming in the adjoint representation, for which we perform numerical investigations at three values of the lattice spacing. The purpose of our study is to advance the characterisation of the infrared properties of both theories, which previous investigations have concluded to be in the conformal window. For both, we determine the mass spectrum and the anomalous dimension of the fermion condensate using finite-size hyperscaling of the spectrum, mode number analysis of the Dirac operator (for which we improve on our previous proposal) and the ratio of masses of the lightest spin-2 particle over the lightest scalar. All methods provide a consistent picture, with the anomalous dimension of the condensate $\gamma_*$ decreasing significantly as one approaches the continuum limit for the $N_{\mathrm{f}} = 1$ theory towards a value consistent with $\gamma_* = 0.170(6)$, while for $N_{\mathrm{f}} = 2$ the anomalous dimension converges more rapidly with $\beta$ to a value of $\gamma_* = 0.291(9)$. A chiral perturbation theory analysis shows that the infrared behaviour of both theories is incompatible with the breaking of chiral symmetry.