The slowly evolving gauge coupling of gauge-fermion systems near the conformal window makes numerical investigations of these models challenging. We consider finite size scaling and show that this often used technique leads to inconsistent results if the leading order scaling corrections are neglected. When the corrections are included the results become consistent not only between different operators but even when data obtained at different gauge couplings or with different lattice actions are combined. Our results indicate that the SU(3) 12-fermion system is conformal with mass anomalous dimension γm = 0.235(15).

We present our lattice studies of SU(3) gauge theory with N f = 8 degenerate fermions in the fundamental representation. Using nHYP-smeared staggered fermions we study finite-temperature transitions on lattice volumes as large as L 3 ×Nt = 48 3 ×24, and the zero-temperature composite spectrum on lattice volumes up to 64 3 ×128. The spectrum indirectly indicates spontaneous chiral symmetry breaking, but finite-temperature transitions with fixed Nt ≤ 24 enter a strongly coupled lattice phase as the fermion mass decreases, which prevents a direct confirmation of spontaneous chiral symmetry breaking in the chiral limit. In addition to the connected spectrum we focus on the lightest flavor-singlet scalar particle. We find it to be degenerate with the pseudo-Goldstone states down to the lightest masses reached so far by non-perturbative lattice calculations. Using the same lattice approach, we study the behavior of the composite spectrum when the number of light fermions is changed from eight to four. A heavy flavor-singlet scalar in the 4-flavor theory affirms the contrast between QCD-like dynamics and the low-energy behavior of the 8-flavor theory. *

We study the phase structure of SU(3) lattice gauge theory with N f = 12 staggered fermions in the fundamental representation, for both zero and finite temperature at strong gauge couplings. For small fermion masses we find two transitions at finite temperature that converge to two wellseparated bulk phase transitions. The phase between the two transitions appears to be a novel phase. We identify order parameters showing that the single-site shift symmetry of staggered fermions is spontaneously broken in this phase. We investigate the eigenvalue spectrum of the Dirac operator, the static potential and the meson spectrum, which collectively establish that this novel phase is confining but chirally symmetric. The phase is bordered by first-order phase transitions, and since we find the same phase structure with N f = 8 fermions, we argue that the novel phase is most likely a strong-coupling lattice artifact, the existence of which does not imply IR conformality.

We present results for the spectrum of a strongly interacting SU(3) gauge theory with $N_f = 8$ light fermions in the fundamental representation. Carrying out non-perturbative lattice calculations at the lightest masses and largest volumes considered to date, we confirm the existence of a remarkably light singlet scalar particle. We explore the rich resonance spectrum of the 8-flavor theory in the context of the search for new physics beyond the standard model at the Large Hadron Collider (LHC). Connecting our results to models of dynamical electroweak symmetry breaking, we estimate the vector resonance mass to be about 2 TeV with a width of roughly 450 GeV, and predict additional resonances with masses below ~3 TeV.Comment: 6 pages, 6 figures. Added report number. Version submitted to journa

We examine several recent lattice-simulation data sets, asking whether they are consistent with infrared conformality. We observe, in particular, that for an SU (3) gauge theory with 12 Dirac fermions in the fundamental representation, recent simulation data can be described assuming infrared conformality. Lattice simulations include a fermion mass m which is then extrapolated to zero, and we note that this data can be fit by a small-m expansion, allowing a controlled extrapolation. We also note that the conformal hypothesis does not work well for two theories that are known or expected to be confining and chirally broken, and that it does work well for another theory expected to be infrared conformal.

Maximally supersymmetric Yang-Mills theory in four dimensions can be formulated on a spacetime lattice while exactly preserving a single supersymmetry. Here we explore in detail this lattice theory, paying particular attention to its strongly coupled regime. Targeting a theory with gauge group SU(N ), the lattice formulation is naturally described in terms of gauge group U(N ). Although the U(1) degrees of freedom decouple in the continuum limit we show that these degrees of freedom lead to unwanted lattice artifacts at strong coupling. We demonstrate that these lattice artifacts can be removed, leaving behind a lattice formulation based on the SU(N ) gauge group with the expected apparently conformal behavior at both weak and strong coupling.

We investigate the eigenmodes of the massless Dirac operator to extract the scale-dependent fermion mass anomalous dimension gamma_m(mu). By combining simulations on multiple lattice volumes, and when possible several gauge couplings, we are able to measure the anomalous dimension across a wide range of energy scales. The method that we present is universal and can be applied to any lattice model of interest, including both conformal or chirally broken systems. We consider SU(3) lattice gauge theories with Nf=4, 8 and 12 light or massless fermions. The 4-flavor model behaves as expected for a QCD-like system and demonstrates that systematic effects are manageable in practical lattice calculations. Our 12-flavor results are consistent with the existence of an infrared fixed point, at which we predict the scheme-independent mass anomalous dimension gamma_m^*=0.32(3). For the 8-flavor model we observe a large anomalous dimension across a wide range of energy scales. Further investigation is required to determine whether Nf=8 is chirally broken and walking, or if it possesses a strongly-coupled conformal fixed point.Comment: Version to be published in JHE

We introduce a non-perturbative improvement for the renormalization group step scaling function based on the gradient flow running coupling, which may be applied to any lattice gauge theory of interest. Considering first SU(3) gauge theory with N f = 4 massless staggered fermions, we demonstrate that this improvement can remove O(a 2 ) lattice artifacts, and thereby increases our control over the continuum extrapolation. Turning to the 12-flavor system, we observe an infrared fixed point in the infinite-volume continuum limit. Applying our proposed improvement reinforces this conclusion by removing all observable O(a 2 ) effects. For the finite-volume gradient flow renormalization scheme defined by c = √ 8t/L = 0.2, we find the continuum conformal fixed point to be located at g 2 = 6.2(2).