arXiv subjects

Masanori Okawa

Publications and source records attributed to Masanori Okawa.

51 records · Page 3Linked to original sources

arXiv2013

Twisted reduction in large N QCD with adjoint Wilson fermions

The twisted space-time reduced model of large $N$ QCD with various flavours of adjoint Wilson fermions is constructed applying the symmetric twist boundary conditions with flux $k$. The models with one and two flavours show distinctive behaviours. For the two flavor case, the string tension, calculated at $N=289$, approaches zero as we decrease the quark mass in a way consistent with the theory being governed by an infrared fixed point. In contrast, the string tension for the case of a single adjoint Wilson fermion remains finite as the quark mass decreases to zero, supporting that this is a confining theory.

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arXiv2013

Perturbative analysis of twisted volume reduced theories

We discuss the perturbative expansion of SU(N) Yang-Mills theories defined on a d-dimensional torus of linear size l with twisted boundary conditions, generalizing previous results in the literature. For a specific class of twist tensors depending on a single integer flux value k, we show that perturbative results to all orders depend on the combination lN^(2/d) and a flux-dependent angle theta. This implies a new kind of volume independence that holds at finite N and for fixed values of theta. Our results also provide interesting information about the possible occurrence of tachyonic instabilities at one-loop order. We support the prescription that instabilities are avoided, if the large N limit is taken keeping theta > theta_c, and appropriately scaling the magnetic flux k with N. Numerical results in 2+1 dimensions provide a test of how these ideas extend into the non-perturbative regime.

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arXiv2013

Mass anomalous dimension from large N twisted volume reduction

In this work we consider the SU(N) gauge theory with two Dirac fermions in the adjoint representation, in the limit of large N. Taking advantage of large N twisted volume reduction we do this on a single site lattice, but we should still get infinite-volume physics in the large N limit. We describe our progress in extracting the mass anomalous dimension from the eigenvalue distribution of the adjoint Dirac operator, using data for N up to 289.

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arXiv2013

Spatial volume dependence for 2+1 dimensional SU(N) Yang-Mills theory

We study the 2+1 dimensional SU(N) Yang-Mills theory on a finite two-torus with twisted boundary conditions. Our goal is to study the interplay between the rank of the group N, the length of the torus L and the Z_N magnetic flux. After presenting the classical and quantum formalism, we analyze the spectrum of the theory using perturbation theory to one-loop and using Monte Carlo techniques on the lattice. In perturbation theory, results to all orders depend on the combination x=λNL and an angle defined in terms of the magnetic flux (λ is 't Hooft coupling). Thus, fixing the angle, the system exhibits a form of volume independence (NL dependence). The numerical results interpolate between our perturbative calculations and the confinement regime. They are consistent with x-scaling and provide interesting information about the k-string spectrum and effective string theories. The occurrence of tachyonic instabilities is also analysed. They seem to be avoidable in the large N limit with a suitable scaling of the magnetic flux.

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arXiv2013

Twisted space-time reduced model of large N QCD with two adjoint Wilson fermions

The space-time reduced model of large N QCD with two adjoint Wilson fermions is constructed by applying the symmetric twist boundary conditions with non-vanishing flux $k$. For large but finite $N=L^2$, the model should behave as the large N version of the ordinary lattice gauge model on a $V=L^4$ space-time volume. We perform a comparison of the $N$ dependence of several quantities in this model and in the $k$=0 model (corresponding to periodic boundary conditions). Although the Z$^4$(N) symmetry seems unbroken in all cases, the N-dependence analysis favours the use of the same values of $k$ and $L$ for which the symmetry is also unbroken in the pure gauge case. In particular, the $k=0$ model, studied recently by several authors, shows a large and irregular dependence on $N$ within our region of parameters. This makes this reduced model very impractical for extracting physical information about the large N lattice theory. On the contrary, the model for $N=289=17^2$ and large enough $k$ gives consistent results, even for extended observables as Wilson loops $W(R,T)$ up to $R,T$=8, matching the expected behaviour for the lattice model with a $17^4$ space-time volume.

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arXiv2013

Twisted reduction in large $N$ QCD with adjoint Wilson fermions

The twisted reduced model of large $N$ QCD with two adjoint Wilson fermions is studied numerically using the Hybrid Monte Carlo method. This is the one-site model, whose large $N$ limit (large volume limit) is expected to be conformal or nearly conformal. The string tension calculated at $N$=289 approaches zero as we decrease quark mass and the preliminary value of the mass anomalous dimension $γ_*$ is close to one if we assume that the theory is governed by an infrared fixed point. We also discuss the twisted reduced model with single adjoint Wilson fermion. The string tension remains finite as the quark mass decreases to zero, supporting that this is the confining theory.

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arXiv2013

Confinement in large N gauge theories

We report some recent results obtained for large N gauge theories which support the idea of volume reduction. Results for the string tension of the Twisted Eguchi-Kawai model match with those obtained from extrapolation from finite N. Determination of other observables is currently under way. Application of the twisted reduction idea to the case of 1 or 2 flavours of quarks in the adjoint representation of the group offers promising results. Preliminary results for the string tension point towards a very different behaviour for 1 and 2 flavours. While the string tension remains finite for 1 flavour at the critical massless quark limit, it seems to vanish with a large anomalous dimension for the $N_f=2$ case. This is consistent with the predicted Infrared fixed point expected in the latter case.

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arXiv2013

The string tension from smeared Wilson loops at large N

We present the results of a high statistics analysis of smeared Wilson loops in 4 dimensional SU(N) Yang-Mills theory for various values of N. The data is used to analyze the behaviour of smeared Creutz ratios, extracting from them the value of the string tension and other asymptotic parameters. A scaling analysis allows us to extrapolate to the continuum limit for N=3,5,6 and 8. The results are consistent with a $1/N^2$ approach towards the large N limit. The same analysis is done for the TEK model (one-point lattice) for N=841 and a non-minimal symmetric twist with flux of $k=9$. The results match perfectly with the extrapolated large N values, confirming the validity of the reduction idea for this range of parameters.

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arXiv2012

The string tension for Large N gauge theory from smeared Wilson loops

Using smeared Creutz ratios we extract the string tension for SU(N) pure gauge theory and $N$=3,4,5,6,8. We employ these results to extrapolate to large N. The same methodology is applied to the single-site Twisted Eguchi Kawai model. The corresponding string tension matches perfectly within errors with the extrapolated one, providing strong evidence in favour of the twisted reduction framework. Interesting results are also obtained on the behaviour of Creutz ratios for large sizes.

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arXiv2012

Volume dependence in 2+1 Yang-Mills theory

We present the results of an analysis of a 2+1 dimensional pure SU(N) Yang-Mills theory formulated on a 2-dimensional spatial torus with non-trivial magnetic flux. We focus on investigating the dependence of the electric-flux spectrum, extracted from Polyakov loop correlators, with the spatial size l, the number of colours N, and the magnetic flux m. The size of the torus acts a parameter that allows to control the onset of non-perturbative effects. In the small volume regime, where perturbation theory holds, we derive the one-loop self-energy correction to the single-gluon spectrum, for arbitrary N and m. We discuss the transition from small to large volumes that has been investigated by means of Monte-Carlo simulations. We argue that the energy of electric flux e, for the lowest gluon momentum, depends solely on e/N and on the dimensionless variable x=lambda N l, with lambda the 't Hooft coupling. The variable x can be interpreted as the dimensionless 't Hooft coupling for an effective box size given by Nl. This implies a version of reduction that allows to trade l by N without modifying the electric-flux energy.

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arXiv2012

Twisted reduction in large N QCD with two adjoint Wilson fermions

The twisted reduced model of large $N$ QCD with two adjoint Wilson fermions is studied numerically using the Hybrid Monte Carlo method. This is the one-site model, whose large $N$ limit (large volume limit) is expected to be conformal or nearly conformal. The symmetric twist boundary condition with flux $k$ is used. $k$=0 corresponds to periodic boundary conditions. It is shown that the quark mass and $N$ dependencies of the model with non-vanishing $k$ differ significantly from those of the $k$=0 model. A preliminary result for the string tension calculated at $N$=289 is presented. The string tension seems to vanish as the physical quark mass decreases to zero in a way consistent with the theory being governed by an infrared fixed point with $γ_* = 0.8 \sim 1.2$.

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arXiv2010

Large $N$ reduction with the Twisted Eguchi-Kawai model

We examine the breaking of $Z_N$ symmetry recently reported for the Twisted Eguchi-Kawai model (TEK). We analyse the origin of this behaviour and propose simple modifications of twist and lattice action that could avoid the problem. Our results show no sign of symmetry breaking and allow us to obtain values of the large $N$ infinite volume string tension in agreement with extrapolations from results based upon straightforward methods.

hep-th↗

arXiv2004

Anisotropic lattice with nonperturbative accuracy

We determine the nonperturbative anisotropic parameter of the gauge action in the quenched approximation with less than 1% accuracy using the Sommer scale measured by the Lüscher-Weisz algorithm or smearing technique. We also study the nonperturbative O(a)-improvement of the quark action. The bare quark anisotropy is determined using the masses from the temporal and spatial directions. For the determination of the $O(a)$ improvement coefficients, we apply the Schrödinger functional method.

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arXiv2003

Anisotropic lattices for precision computations in heavy flavor physics

We study the anisotropic lattice QCD for precision computations of heavy-light matrix elements. Our previous study in which the lattices are calibrated with a few percent accuracy has already given results comparable to the existing calculations. This suggests that even higher precision may be achieved by a more precise calibration of anisotropic lattices. We describe our strategy to tune the gauge and quark parameters with accuracies much less than 1 % in the quenched approximation.

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arXiv1995

New Developments in Lattice QCD: Calculation of Flavor Singlet Nucleon Matrix Elements and Hadron Scattering Lengths

Recent developments in lattice QCD calculation of flavor singlet nucleon matrix elements are reviewed. Substantial sea quark contributions are found in the $π$-$N\ σ$ term and the quark spin content of the nucleon such that the total magnitude including valence contributions is in reasonable agreement with experiments. Some problems with flavor non-singlet nucleon matrix elements are pointed out. Recent work on lattice QCD calculation of hadron scattering length is also discussed.

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