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

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 ${\gamma }_{\ast }$ decreasing significantly as one approaches the continuum limit for the $N_{\mathrm{f}}=1$ theory towards a value consistent with ${\gamma }_{\ast }=0.170(6)$, while for $N_{\mathrm{f}}=2$ the anomalous dimension converges more rapidly with $\beta$ to a value of ${\gamma }_{\ast }=0.291(9)$. A chiral perturbation theory analysis shows that the infrared behaviour of both theories is incompatible with the breaking of chiral symmetry.

Comments: 31 pages, 31 figures. Version accepted for publication in Physical Review D, including additional ensembles at additional values of $\beta$ for the $N_{\mathrm{f}}=2$ theory, and an update to the estimate of the anomalous dimension continuum limit resulting from this. Other conclusions unchanged