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

We estimate a possibleη′gluonic contribution to the self-energy of a nucleon in an effective theory. The couplings of the topological charge density to nucleons give rise to OZI violatingη′-nucleon interactions. The one-loop self-energy of nucleon arising due to these interactions is studied using a heavy baryon chiral perturbation theory. The divergences have been removed using appropriate form factors. The nontrivial structure of the QCD vacuum has also been taken into account. The numerical results are sensitive to the choice of the regulator to a nonnegligible extent. We get the total contribution to the nucleon mass coming from its interaction with the topological charge densityδmtot≅-(2.5–7.5)% of the nucleon mass.

Download Full-text

Topological charge density waves at half-integer filling of a moiré superlattice

Nature Physics ◽

10.1038/s41567-021-01418-6 ◽

2021 ◽

Author(s):

H. Polshyn ◽

Y. Zhang ◽

M. A. Kumar ◽

T. Soejima ◽

P. Ledwith ◽

...

Keyword(s):

Charge Density ◽

Topological Charge ◽

Charge Density Waves ◽

Density Waves ◽

Half Integer

Download Full-text

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

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09837-8 ◽

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).

Download Full-text

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

Progress of Theoretical and Experimental Physics ◽

10.1093/ptep/ptaa138 ◽

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.

Download Full-text

Image-processing the topological charge density in the $\mathbb{C}P^{N-1}$ model

Progress of Theoretical and Experimental Physics ◽

10.1093/ptep/ptz134 ◽

2020 ◽

Vol 2020 (1) ◽

Cited By ~ 2

Author(s):

Yuya Abe ◽

Kenji Fukushima ◽

Yoshimasa Hidaka ◽

Hiroaki Matsueda ◽

Koichi Murase ◽

...

Keyword(s):

Charge Density ◽

Topological Charge ◽

Distribution Patterns ◽

Singular Value ◽

Power Spectrum Analysis ◽

Topological Properties ◽

Inverse Temperature ◽

Charge Density Distribution ◽

Coupling Analysis ◽

Value Decomposition

Abstract We study the topological charge density distribution using the 2D $\mathbb{C}P^{N-1}$ model. We numerically compute not only the topological susceptibility, which is a spatially global quantity, to probe the topological properties of the whole system, but also the topological charge correlator with finite momentum. We perform a Fourier power spectrum analysis for the topological charge density for various values of the inverse temperature $\beta$. We propose to utilize the Fourier entropy as a convenient measure to characterize spatial distribution patterns and demonstrate that the Fourier entropy exhibits nontrivial temperature dependence. We also consider the snapshot entropy defined with the singular value decomposition, which also turns out to behave nonmonotonically with the temperature. We give a possible interpretation suggested from the strong-coupling analysis.

Download Full-text