6,007 research outputs found

    Improved Lattice Renormalization Group Techniques

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    We compute the bare step-scaling function sbs_b for SU(3) lattice gauge theory with Nf=12N_f = 12 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 sbs_b corresponding to a unique discrete β\beta 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 32432^4. 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

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    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 γm=0.25\gamma_m=0.25.Comment: Contribution to 31st International Symposium on Lattice Field Theory - LATTICE 201

    Determining the mass anomalous dimension through the eigenmodes of Dirac operator

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    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 γm\gamma_m of an asymptotically-free system to the universal γm\gamma_m^{\star} 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 48448^4. Focusing on SU(3) lattice gauge theory with Nf=12N_f = 12 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 γm0.25\gamma_m^{\star} \approx 0.25. 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

    Scale-dependent mass anomalous dimension from Dirac eigenmodes

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    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

    Reaching the chiral limit in many flavor systems

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    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

    Complete Analysis of Netflix, Inc.

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    This thesis focuses on the company, Netflix, INC and the projected value of this company. This study provides valuable information regarding the projected value of Netflix, INC and future stock price predictions. I derived my findings through several procedures. The most important procedure in analyzing the future value of Netflix was the use of a Discounted Cash Flow Analysis. This analysis provided me with a projected value and share price for Netflix, INC in five years and again in ten years. The second method used to evaluate Netflix was the multiples valuation. This method provided information on whether or not Netflix is overvalued or undervalued. I also analyzed the industry in general and provided information regarding Netflix’s strengths and weaknesses. To summarize my findings, I believe that Netflix is, for the most part, on the overvalued spectrum. This is proven through my multiples valuation. This statement is supported by my DCF valuation as well. Netflix’s value and share price are projected to increase over the next five years, but then will face a down turn be year ten (2030). This will cause Netflix’s value to decline as well as its share price. In conclusion, I would recommend holding NFLX stocks until 2025, then selling to receive maximum prophetization. If you do not currently own Netflix stock, I would recommend buying now and also selling around 2025 to make a profit