scholarly journals Classifying Topological Charge in SU(3) Yang-Mills Theory with Machine Learning

2020 ◽  
Author(s):  
Takuya Matsumoto ◽  
Masakiyo Kitazawa ◽  
Yasuhiro Kohno
Keyword(s):  
Machine Learning ◽  
Charge Density ◽  
Topological Charge ◽  
Dimensional Space ◽  
Gradient Flow ◽  
Fully Integrated ◽  
Yang Mills ◽  
Physical Volume ◽  
Spatial Coordinates ◽  
Small Flow

Abstract We apply a machine learning technique for identifying the topological charge of quantum gauge configurations in four-dimensional SU(3) Yang-Mills theory. The topological charge density measured on the original and smoothed gauge configurations with and without dimensional reduction is used for inputs of the neural networks (NN) with and without convolutional layers. The gradient flow is used for the smoothing of the gauge field. We find that the topological charge determined at a large flow time can be predicted with high accuracy from the data at small flow times by the trained NN; for example, the accuracy exceeds 99% with the data at t/a2 ≤ 0.3. High robustness against the change of simulation parameters is also confirmed with a fixed physical volume. We find that the best performance is obtained when the spatial coordinates of the topological charge density are fully integrated out as a preprocessing, which implies that our convolutional NN does not find characteristic structures in multi-dimensional space relevant for the determination of the topological charge.

scholarly journals Non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$-dimensional Yang–Mills theory

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
Fabrizio Canfora
Keyword(s):  
Scalar Field ◽  
Charge Density ◽  
Topological Charge ◽  
Conformal Symmetry ◽  
Analytic Solutions ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Field Equations ◽  
Yang Mills ◽  
Non Linear

AbstractAn infinite-dimensional family of analytic solutions in pure SU(2) Yang–Mills theory at finite density in $$(3+1)$$ ( 3 + 1 ) dimensions is constructed. It is labelled by two integeres (p and q) as well as by a two-dimensional free massless scalar field. The gauge field depends on all the 4 coordinates (to keep alive the topological charge) but in such a way to reduce the (3+1)-dimensional Yang–Mills field equations to the field equation of a 2D free massless scalar field. For each p and q, both the on-shell action and the energy-density reduce to the action and Hamiltonian of the corresponding 2D CFT. The topological charge density associated to the non-Abelian Chern–Simons current is non-zero. It is possible to define a non-linear composition within this family as if these configurations were “Lego blocks”. The non-linear effects of Yang–Mills theory manifest themselves since the topological charge density of the composition of two solutions is not the sum of the charge densities of the components. This leads to an upper bound on the amplitudes in order for the topological charge density to be well-defined. This suggests that if the temperature and/or the energy is/are high enough, the topological density of these configurations is not well-defined anymore. Semiclassically, one can show that (depending on whether the topological charge is even or odd) some of the operators appearing in the 2D CFT should be quantized as Fermions (despite the Bosonic nature of the classical field).

scholarly journals SU(3) Yang Mills theory at small distances and fine lattices

2018 ◽  
Vol 175 ◽  
pp. 14024 ◽  
Author(s):  
Nikolai Husung ◽  
Mateusz Koren ◽  
Philipp Krah ◽  
Rainer Sommer
Keyword(s):  
Gradient Flow ◽  
Flow Time ◽  
Open Boundary ◽  
Static Force ◽  
Open Boundary Conditions ◽  
Yang Mills ◽  
Action Density ◽  
Small Flow ◽  
Time Expansion ◽  
Β Function

We investigate the SU(3) Yang Mills theory at small gradient flow time and at short distances. Lattice spacings down to a = 0.015 fm are simulated with open boundary conditions to allow topology to flow in and out. We study the behaviour of the action density E(t) close to the boundaries, the feasibility of the small flow-time expansion and the extraction of the Λ-parameter from the static force at small distances. For the latter, significant deviations from the 4-loop perturbative β-function are visible at α ≈ 0.2. We still can extrapolate to extract roΛ.

scholarly journals Finding the deconfinement temperature in lattice Yang-Mills theories from outside the scaling window with machine learning

2021 ◽  
Vol 103 (1) ◽  
Author(s):  
D. L. Boyda ◽  
M. N. Chernodub ◽  
N. V. Gerasimeniuk ◽  
V. A. Goy ◽  
S. D. Liubimov ◽  
...  
Keyword(s):  
Machine Learning ◽  
Yang Mills ◽  
Scaling Window

FINITE ENERGY ONE-HALF MONOPOLE SOLUTIONS

2012 ◽  
Vol 27 (40) ◽  
pp. 1250233 ◽  
Author(s):  
ROSY TEH ◽  
BAN-LOONG NG ◽  
KHAI-MING WONG
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Flux ◽  
Topological Charge ◽  
Magnetic Monopole ◽  
Magnetic Charge ◽  
Finite Energy ◽  
Spatial Infinity ◽  
Yang Mills ◽  
The Magnetic Field

We present finite energy SU(2) Yang–Mills–Higgs particles of one-half topological charge. The magnetic fields of these solutions at spatial infinity correspond to the magnetic field of a positive one-half magnetic monopole at the origin and a semi-infinite Dirac string on one-half of the z-axis carrying a magnetic flux of [Formula: see text] going into the origin. Hence the net magnetic charge is zero. The gauge potentials are singular along one-half of the z-axis, elsewhere they are regular.

scholarly journals The scaling dimension of low lying Dirac eigenmodes and of the topological charge density

2005 ◽  
Vol 140 ◽  
pp. 626-628 ◽  
Author(s):  
C. Aubin ◽  
C. Bernard ◽  
Steven Gottlieb ◽  
E.B. Gregory ◽  
Urs M. Heller ◽  
...  
Keyword(s):  
Charge Density ◽  
Topological Charge ◽  
Scaling Dimension

scholarly journals About renormalized effective action for the Yang-Mills theory in four-dimensional space-time

2018 ◽  
Vol 191 ◽  
pp. 06001
Author(s):  
A.V. Ivanov
Keyword(s):  
Infinite Series ◽  
Effective Action ◽  
Dimensional Space ◽  
Space Time ◽  
Coupling Constant ◽  
Asymptotic Approach ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Bare Coupling Constant ◽  
Renormalization Theory

This work is related to the asymptotic approach in the renormalization theory and its problems. As the main example, the Yang-Mills theory in four-dimensional space-time is considered. It has been shown earlier [16] that using the asymptotic of the bare coupling constant one can find an expression for the renormalized effective action, however, this formula has problems (divergence ln " and infinite series). This work shows the relation of these values and provides an answer for the renormalized effective action.

scholarly journals Localization of topological charge density near Tc in quenched QCD with Wilson flow

2018 ◽  
Vol 98 (1) ◽  
Author(s):  
You-Hao Zou ◽  
Jian-Bo Zhang ◽  
Guang-Yi Xiong
Keyword(s):  
Charge Density ◽  
Topological Charge
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