64 research outputs found
Improved Lattice Renormalization Group Techniques
We compute the bare step-scaling function for SU(3) lattice gauge
theory with massless fundamental fermions, using the
non-perturbative Wilson-flow-optimized Monte Carlo Renormalization Group
two-lattice matching technique. We use a short Wilson flow to approach the
renormalized trajectory before beginning RG blocking steps. By optimizing the
length of the Wilson flow, we are able to determine an corresponding to a
unique discrete function, after a few blocking steps. We carry out this
study using new ensembles of 12-flavor gauge configurations generated with
exactly massless fermions, using volumes up to . The results are
consistent with the existence of an infrared fixed point (IRFP) for all
investigated lattice volumes and number of blocking steps. We also compare
different renormalization schemes, each of which indicates an IRFP at a
slightly different value of the bare coupling, as expected for an IR-conformal
theory.Comment: 31st International Symposium on Lattice Field Theory, Lattice201
Finite size scaling and the effect of the gauge coupling in 12 flavor systems
Finite size scaling is a powerful tool to study the critical properties of
systems governed by one relevant operator, assuming all irrelevant operators
have scaling dimensions much smaller then zero. This condition is likely not
satisfied in many-fermion conformal systems where perturbation theory predicts
a nearly-marginal irrelevant gauge coupling. In this work we carry out a new
investigation of SU(3) lattice gauge theory with 12 fundamental flavors.
Analyzing data at many different gauge couplings, our preliminary results
indicate that a finite size scaling analysis that takes into account the effect
of a nearly-marginal gauge coupling can resolve many of the inconsistencies
observed previously in this system, leading to results consistent with
conformal infrared dynamics and predicting a mass scaling anomalous around
.Comment: Contribution to 31st International Symposium on Lattice Field Theory
- LATTICE 201
Scale-dependent mass anomalous dimension from Dirac eigenmodes
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
Determining the mass anomalous dimension through the eigenmodes of Dirac operator
We define a scale-dependent effective mass anomalous dimension from the
scaling of the mode number of the massless Dirac operator, which connects the
perturbative of an asymptotically-free system to the universal
at a conformal fixed point. We use a stochastic algorithm to
measure the mode number up to the cutoff scale on lattices as large as .
Focusing on SU(3) lattice gauge theory with massless fundamental
fermions, we examine systematic effects due to finite volumes and non-zero
fermion masses. Our results suggest the existence of an infrared fixed point
with . Our method provides a unique probe to
study systems from the UV to the IR. It is universal and can be applied to any
lattice model of interest, including both chirally-broken and IR-conformal
systems.Comment: 7 pages, 3 figure
Reaching the chiral limit in many flavor systems
We present a brief overview of our recent lattice studies of SU(3) gauge
theory with N_f = 8 and 12 fundamental fermions, including some new and
yet-unpublished results.
To explore relatively unfamiliar systems beyond lattice QCD, we carry out a
wide variety of investigations with the goal of synthesizing the results to
better understand the non-perturbative dynamics of these systems.
All our findings are consistent with conformal infrared dynamics in the
12-flavor system, but with 8 flavors we observe puzzling behavior that requires
further investigation.
Our new Monte Carlo renormalization group technique exploits the Wilson flow
to obtain more direct predictions of a 12-flavor IR fixed point.
Studies of N_f = 12 bulk and finite-temperature transitions also indicate IR
conformality, while our current results for the 8-flavor phase diagram do not
yet provide clear signs of spontaneous chiral symmetry breaking.
From the Dirac eigenvalue spectrum we extract the mass anomalous dimension
gamma_m, and predict gamma*_m = 0.32(3) at the 12-flavor fixed point.
The N_f = 8 system again shows interesting behavior, with a large anomalous
dimension across a wide range of energy scales.
We use the eigenvalue density to predict the chiral condensate, and compare
this approach with direct and partially-quenched measurements.Comment: 7 pages, 5 figures; Contribution to SCGT12 "KMI-GCOE Workshop on
Strong Coupling Gauge Theories in the LHC Perspective", 4-7 Dec. 2012, Nagoya
Universit
Improving the continuum limit of gradient flow step scaling
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 massless staggered fermions, we demonstrate that this
improvement can remove 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 effects. For the finite-volume gradient flow
renormalization scheme defined by , we find the
continuum conformal fixed point to be located at Comment: 12 pages, 4 figures; Minor changes, published versio
Finite size scaling of conformal theories in the presence of a near-marginal operator
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
Bulk and finite-temperature transitions in SU(3) gauge theories with many light fermions
We investigate finite-temperature transitions in SU(3) lattice gauge theories
with Nf=8 and 12 staggered fermions in the fundamental representation. For both
of these systems, we have observed a strongly-coupled lattice phase in which
the single-site shift symmetry of the staggered action is spontaneously broken.
Here we report new results for finite-temperature transitions on 24^3x12 and
32^3x16 lattice volumes, contrasting the 8- and 12-flavor systems. While the
Nf=12 finite-temperature transitions accumulate at the bulk transition bounding
the strongly-coupled lattice phase, the Nf=8 finite-temperature transitions are
able to pass through the bulk transition, and behave as expected for a QCD-like
system. We discuss our current results and the work in progress to complete our
investigation of the finite-temperature phase diagram.Comment: Contribution to the proceedings of Lattice 2012, June 24-29, Cairns,
Australia. 7 page
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