Ergodic sampling of the topological charge using the density of states

AbstractIn lattice calculations, the approach to the continuum limit is hindered by the severe freezing of the topological charge, which prevents ergodic sampling in configuration space. In order to significantly reduce the autocorrelation time of the topological charge, we develop a density of states approach with a smooth constraint and use it to study SU(3) pure Yang Mills gauge theory near the continuum limit. Our algorithm relies on simulated tempering across a range of couplings, which guarantees the decorrelation of the topological charge and ergodic sampling of topological sectors. Particular emphasis is placed on testing the accuracy, efficiency and scaling properties of the method. In their most conservative interpretation, our results provide firm evidence of a sizeable reduction of the exponent z related to the growth of the autocorrelation time as a function of the inverse lattice spacing.

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Large N scaling and factorization in SU(N) Yang-Mills theory

EPJ Web of Conferences ◽

10.1051/epjconf/201817511018 ◽

2018 ◽

Vol 175 ◽

pp. 11018 ◽

Cited By ~ 2

Author(s):

Miguel García Vera ◽

Rainer Sommer

Keyword(s):

Lattice Spacing ◽

Continuum Limit ◽

Finite Lattice ◽

Gradient Flow ◽

Scaling Up ◽

Wilson Loops ◽

Yang Mills ◽

Large N ◽

The Continuum

We present results for Wilson loops smoothed with the Yang-Mills gradient flow and matched through the scale t0. They provide renormalized and precise operators allowing to test the 1/N2 scaling both at finite lattice spacing and in the continuum limit. Our results show an excellent scaling up to 1/N = 1/3. Additionally, we obtain a very precise non-perturbative confirmation of factorization in the large N limit.

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From Center-Vortex Ensembles to the Confining Flux Tube

Universe ◽

10.3390/universe7080253 ◽

2021 ◽

Vol 7 (8) ◽

pp. 253

Author(s):

David R. Junior ◽

Luis E. Oxman ◽

Gustavo M. Simões

Keyword(s):

Degrees Of Freedom ◽

String Tension ◽

Effective Field ◽

Scaling Properties ◽

Flux Tubes ◽

Topological Solitons ◽

Yang Mills ◽

Center Vortex ◽

Asymptotic Scaling ◽

The Continuum

In this review, we discuss the present status of the description of confining flux tubes in SU(N) pure Yang–Mills theory in terms of ensembles of percolating center vortices. This is based on three main pillars: modeling in the continuum the ensemble components detected in the lattice, the derivation of effective field representations, and contrasting the associated properties with Monte Carlo lattice results. The integration of the present knowledge about these points is essential to get closer to a unified physical picture for confinement. Here, we shall emphasize the last advances, which point to the importance of including the non-oriented center-vortex component and non-Abelian degrees of freedom when modeling the center-vortex ensemble measure. These inputs are responsible for the emergence of topological solitons and the possibility of accommodating the asymptotic scaling properties of the confining string tension.

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Testing algorithms for critical slowing down

EPJ Web of Conferences ◽

10.1051/epjconf/201817502008 ◽

2018 ◽

Vol 175 ◽

pp. 02008 ◽

Cited By ~ 3

Author(s):

Guido Cossu ◽

Peter Boyle ◽

Norman Christ ◽

Chulwoo Jung ◽

Andreas Jüttner ◽

...

Keyword(s):

Monte Carlo ◽

Topological Charge ◽

Continuum Limit ◽

Critical Slowing Down ◽

Gauge Fields ◽

Hybrid Monte Carlo ◽

Slowing Down ◽

Testing Algorithms ◽

New Algorithms ◽

The Continuum

We present the preliminary tests on two modifications of the Hybrid Monte Carlo (HMC) algorithm. Both algorithms are designed to travel much farther in the Hamiltonian phase space for each trajectory and reduce the autocorrelations among physical observables thus tackling the critical slowing down towards the continuum limit. We present a comparison of costs of the new algorithms with the standard HMC evolution for pure gauge fields, studying the autocorrelation times for various quantities including the topological charge.

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On the continuum limit of fermionic topological charge in lattice gauge theory

Journal of Mathematical Physics ◽

10.1063/1.1415087 ◽

2001 ◽

Vol 42 (12) ◽

pp. 5522-5533 ◽

Cited By ~ 31

Author(s):

David H. Adams

Keyword(s):

Gauge Theory ◽

Topological Charge ◽

Continuum Limit ◽

Lattice Gauge Theory ◽

Lattice Gauge ◽

The Continuum

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A STUDY OF GLUON PROPAGATOR ON COARSE LATTICE

Modern Physics Letters A ◽

10.1142/s0217732300000220 ◽

2000 ◽

Vol 15 (04) ◽

pp. 229-244 ◽

Cited By ~ 11

Author(s):

J. P. MA

Keyword(s):

Lattice Qcd ◽

Smooth Function ◽

Qualitative Agreement ◽

Lattice Spacing ◽

Continuum Limit ◽

Gluon Propagator ◽

Landau Gauge ◽

Lattice Action ◽

Lattice Volume ◽

The Continuum

We study gluon propagator in Landau gauge with lattice QCD, where we use an improved lattice action. The calculation of gluon propagator is performed on lattices with the lattice spacing from 0.40 fm to 0.24 fm and with the lattice volume from (2.40 fm )4 to (4.0 fm )4. We find that the rotation invariance is approximately restored in the q2-range, indicated by the fact that the propagator is a smooth function of the continuum momentum q2. We try to fit our results by two different ways, in the first one we interpret the calculated gluon propagators as a function of the continuum momentum, while in the second we interpret the propagators as a function of the lattice momentum. In both cases we use models which are the same in continuum limit. A qualitative agreement between two fittings is found.

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MATRIX REGULARIZATION OF N = 4 SYM ON R × S3

International Journal of Modern Physics A ◽

10.1142/s0217751x08040834 ◽

2008 ◽

Vol 23 (14n15) ◽

pp. 2199-2200 ◽

Cited By ~ 2

Author(s):

GORO ISHIKI

Keyword(s):

Gauge Symmetry ◽

Plane Wave ◽

Regularization Method ◽

Ward Identity ◽

Continuum Limit ◽

Beta Function ◽

Yang Mills ◽

Planar Limit ◽

Matrix Regularization ◽

The Continuum

We revealed a relationship between the plane wave matrix model (PWMM) and N =4 super Yang-Mills (SYM) theory on R × S3: N =4 SYM on R × S3 is equivalent to the theory around a certain vacuum of PWMM. It is suggested from this relation that N =4 SYM on R × S3 is regularized by PWMM in the planar limit. Because PWMM originally possesses the gauge symmetry and SU(2|4) symmetry, this regularization also preserves these symmetries. In order to check the validity of this matrix regularization method, we calculate the Ward identity and the beta function at the 1-loop level. We find that the Ward identity is satisfied and the beta function vanishes in the continuum limit. The former result is consistent with the gauge symmetry of PWMM. The latter suggests the possibility that the conformal symmety is restored in the continuum limit.

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Truncation of lattice N = 4 super Yang-Mills

EPJ Web of Conferences ◽

10.1051/epjconf/201817511008 ◽

2018 ◽

Vol 175 ◽

pp. 11008 ◽

Cited By ~ 1

Author(s):

Joel Giedt ◽

Simon Catterall ◽

Raghav Govind Jha

Keyword(s):

Gauge Theory ◽

Gauge Symmetry ◽

Moduli Space ◽

Lattice Spacing ◽

Continuum Limit ◽

Power Counting ◽

Yang Mills ◽

Free Theory ◽

Lattice Gauge ◽

Two Sectors

In twisted and orbifold formulations of lattice N = 4 super Yang-Mills, the gauge group is necessarily U(1) × SU(N), in order to be consistent with the exact scalar supersymmetry Q. In the classical continuum limit of the theory, where one expands the link fields around a point in the moduli space and sends the lattice spacing to zero, the diagonal U(1) modes decouple from the SU(N) sector, and give an uninteresting free theory. However, lattice artifacts (described by irrelevant operators according to naive power-counting) couple the two sectors, so removing the U(1) modes is a delicate issue. We describe how this truncation to an SU(N) gauge theory can be obtained in a systematic way, with violations of Q that fall off as powers of 1=N2. We are able to achieve this while retaining exact SU(N) lattice gauge symmetry at all N, and provide both theoretical arguments and numerical evidence for the 1=N2 suppression of Q violation.

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