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 Latent heat and pressure gap at the first order deconfining phase transition of SU(3) Yang-Mills theory using the small flow-time expansion method

2020 ◽  
Author(s):  
Mizuki Shirogane ◽  
Shinji Ejiri ◽  
Ryo Iwami ◽  
Kazuyuki Kanaya ◽  
Masakiyo Kitazawa ◽  
...  
Keyword(s):  
Phase Transition ◽  
Energy Density ◽  
Latent Heat ◽  
Flow Time ◽  
Yang Mills ◽  
First Order ◽  
Pressure Gap ◽  
Small Flow ◽  
Time Expansion ◽  
The Continuum

Abstract We study latent heat and pressure gap between the hot and cold phases at the first order deconfining phase transition temperature of the SU(3) Yang-Mills theory. Performing simulations on lattices with various spatial volumes and lattice spacings, we calculate the gaps of the energy density and pressure using the small flow time expansion (SFtX) method. We find that the latent heat Δ ε in the continuum limit is Δ ε /T4 = 1.117 ± 0.040 for the aspect ratio Ns/Nt = 8 and 1.349 ± 0.038 for Ns/Nt = 6 at the transition temperature T = T c. We also confirm that the pressure gap is consistent with zero, as expected from the dynamical balance of two phases at Tc. From hysteresis curves of the energy density near Tc, we show that the energy density in the (metastable) deconfined phase is sensitive to the spatial volume, while that in the confined phase is insensitive. Furthermore, we examine the effect of alternative procedures in the SFtX method — the order of the continuum and the vanishing flow time extrapolations, and also the renormalization scale and higher order corrections in the matching coefficients. We confirm that the final results are all well consistent with each other for these alternatives.

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 Open fishchain in N = 4 Supersymmetric Yang-Mills Theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Nikolay Gromov ◽  
Julius Julius ◽  
Nicolò Primi
Keyword(s):  
Boundary Conditions ◽  
Degrees Of Freedom ◽  
Wilson Line ◽  
Physical Space ◽  
Scalar Fields ◽  
Open Boundary ◽  
Baxter Equation ◽  
Open Boundary Conditions ◽  
Yang Mills ◽  
Feynman Graphs

Abstract We consider a cusped Wilson line with J insertions of scalar fields in $$ \mathcal{N} $$ N = 4 SYM and prove that in a certain limit the Feynman graphs are integrable to all loop orders. We identify the integrable system as a quantum fishchain with open boundary conditions. The existence of the boundary degrees of freedom results in the boundary reflection operator acting non-trivially on the physical space. We derive the Baxter equation for Q-functions and provide the quantisation condition for the spectrum. This allows us to find the non-perturbative spectrum numerically.

scholarly journals Conserved vector current in QCD-like theories and the gradient flow

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Marco Boers ◽  
Elisabetta Pallante
Keyword(s):  
Anomalous Dimension ◽  
Gauge Coupling ◽  
Gradient Flow ◽  
Vector Current ◽  
Flow Time ◽  
Small Time ◽  
Fermion Field ◽  
Small Flow ◽  
Multiplicative Renormalization ◽  
Conserved Vector Current

Abstract We present analytical results for the Euclidean 2-point correlator of the flavor- singlet vector current evolved by the gradient flow at next-to-leading order $$ \left(\mathcal{O}\left({g}^2\right)\right) $$ O g 2 in perturbatively massless QCD-like theories. We show that the evolved 2-point correlator requires multiplicative renormalization, in contrast to the nonevolved case, and confirm, in agreement with other results in the literature, that such renormalization ought to be identified with a universal renormalization of the evolved elementary fermion field in all evolved fermion-bilinear currents, whereas the gauge coupling renormalizes as usual. We explicitly derive the asymptotic solution of the Callan-Symanzik equation for the connected 2-point correlators of these evolved currents in the limit of small gradient-flow time $$ \sqrt{t} $$ t , at fixed separation |x − y|. Incidentally, this computation determines the leading coefficient of the small-time expansion (STE) for the evolved currents in terms of their local nonevolved counterpart. Our computation also implies that, in the evolved case, conservation of the vector current, hence transversality of the corresponding 2-point correlator, is no longer related to the nonrenormalization, in contrast to the nonevolved case. Indeed, for small flow time the evolved vector current is conserved up to $$ \mathcal{O} $$ O (t) softly violating effects, despite its t-dependent nonvanishing anomalous dimension.

scholarly journals Impurity induced scale-free localization

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Linhu Li ◽  
Ching Hua Lee ◽  
Jiangbin Gong
Keyword(s):  
Boundary Conditions ◽  
Skin Effect ◽  
Reciprocal Lattice ◽  
Periodic Boundary Conditions ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Translational Invariance ◽  
Scale Free ◽  
Special Cases ◽  
Simulation Results

AbstractNon-Hermitian systems have been shown to have a dramatic sensitivity to their boundary conditions. In particular, the non-Hermitian skin effect induces collective boundary localization upon turning off boundary coupling, a feature very distinct from that under periodic boundary conditions. Here we develop a full framework for non-Hermitian impurity physics in a non-reciprocal lattice, with periodic/open boundary conditions and even their interpolations being special cases across a whole range of boundary impurity strengths. We uncover steady states with scale-free localization along or even against the direction of non-reciprocity in various impurity strength regimes. Also present are Bloch-like states that survive albeit broken translational invariance. We further explore the co-existence of non-Hermitian skin effect and scale-free localization, where even qualitative aspects of the system’s spectrum can be extremely sensitive to impurity strength. Specific circuit setups are also proposed for experimentally detecting the scale-free accumulation, with simulation results confirming our main findings.

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