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Register a new userLattice study of infrared behaviour in SU(3) gauge theory with twelve massless flavours
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We present details of a lattice study of infrared behaviour in SU(3) gauge theory with twelve massless fermions in the fundamental representation. Using the step-scaling method, we compute the coupling constant in this theory over a large range of scale. The renormalisation scheme in this work is defined by the ratio of Polyakov loops in the directions with different boundary conditions. We closely examine systematic effects, and find that they are dominated by errors arising from the continuum extrapolation. Our investigation suggests that SU(3) gauge theory with twelve flavours contains an infrared fixed point.
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We study the discrete beta function of SU(3) gauge theory with Nf=12 massless fermions in the fundamental representation. Using an nHYP-smeared staggered lattice action and an improved gradient flow running coupling $tilde g_c^2(L)$ we determine the continuum-extrapolated discrete beta function up to $g_c^2 approx 8.2$. We observe an IR fixed point at $g_{star}^2 = 7.3left(_{-2}^{+8}right)$ in the $c = sqrt{8t} / L = 0.25$ scheme, and $g_{star}^2 = 7.3left(_{-3}^{+6}right)$ with c=0.3, combining statistical and systematic uncertainties in quadrature. The systematic effects we investigate include the stability of the $(a / L) to 0$ extrapolations, the interpolation of $tilde g_c^2(L)$ as a function of the bare coupling, the improvement of the gradient flow running coupling, and the discretization of the energy density. In an appendix we observe that the resulting systematic errors increase dramatically upon combining smaller $c lesssim 0.2$ with smaller $L leq 12$, leading to an IR fixed point at $g_{star}^2 = 5.9(1.9)$ in the c=0.2 scheme, which resolves to $g_{star}^2 = 6.9left(_{-1}^{+6}right)$ upon considering only $L geq 16$. At the IR fixed point we measure the leading irrelevant critical exponent to be $gamma_g^{star} = 0.26(2)$, comparable to perturbative estimates.
{We present the results of a numerical investigation of SU(2) gauge theory with $N_f=3/2$ flavours of fermions, corresponding to 3 Majorana fermions, which transform in the adjoint representation of the gauge group. At two values of the gauge coupling, the masses of bound states are considered as a function of the PCAC quark mass. The scaling of bound states masses indicates an infrared conformal behaviour of the theory. We obtain estimates for the fixed-point value of the mass anomalous dimension $gamma^*$ from the scaling of masses and from the scaling of the mode number of the Wilson-Dirac operator.
Using a standard cooling method for SU(3) lattice gauge fields constant Abelian magnetic field configurations are extracted after dyon-antidyon constituents forming metastable Q=0 configurations have annihilated. These so-called Dirac sheets, standard and non-standard ones, corresponding to the two U(1) subgroups of the SU(3) group, have been found to be stable if emerging from the confined phase, close to the deconfinement phase transition, with sufficiently nontrivial Polyakov loop values. On a finite lattice we find a nice agreement of the numerical observations with the analytic predictions concerning the stability of Dirac sheets depending on the value of the Polyakov loop.
An SU(2) gauge theory with two fermions transforming under the adjoint representation of the gauge group may appear conformal or almost conformal in the infrared. We use lattice simulations to study the spectrum of this theory and present results on the masses of several gauge singlet states as a function of the physical quark mass determined through the axial Ward identity and find indications of a change from chiral symmetry breaking to a phase consistent with conformal behaviour at beta_L ~ 2. However, the measurement of the spectrum is not alone sufficient to decisively confirm the existence of conformal fixed point in this theory as we show by comparing to similar measurements with fundamental fermions. Based on the results we sketch a possible phase diagram of this lattice theory and discuss the applicability and importance of these results for the future measurement of the evolution of the coupling constant.
We present new lattice investigations of finite-temperature transitions for SU(3) gauge theory with Nf=8 light flavors. Using nHYP-smeared staggered fermions we are able to explore renormalized couplings $g^2 lesssim 20$ on lattice volumes as large as $48^3 times 24$. Finite-temperature transitions at non-zero fermion mass do not persist in the chiral limit, instead running into a strongly coupled lattice phase as the mass decreases. That is, finite-temperature studies with this lattice action require even larger $N_T > 24$ to directly confirm spontaneous chiral symmetry breaking.
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