scholarly journals Center vortices, area law and the catenary solution

2015 ◽  
Vol 30 (34) ◽  
pp. 1550207 ◽  
Author(s):  
Roman Höllwieser ◽  
Derar Altarawneh
Keyword(s):  
Surface Tension ◽  
Wilson Loop ◽  
Dimensional Model ◽  
Expectation Values ◽  
Yang Mills ◽  
Surface Behavior ◽  
Vortex Lines ◽  
Center Vortex ◽  
Hypercubic Lattice ◽  
Area Law

We present meson–meson (Wilson loop) correlators in Z(2) center vortex models for the infrared sector of Yang–Mills theory, i.e. a hypercubic lattice model of random vortex surfaces and a continuous (2 + 1)-dimensional model of random vortex lines. In particular, we calculate quadratic and circular Wilson loop correlators in the two models, respectively, and observe that their expectation values follow the area law and show string breaking behavior. Further, we calculate the catenary solution for the two cases and try to find indications for minimal surface behavior or string surface tension leading to string constriction.

scholarly journals Double-winding Wilson loops in SU(N) Yang-Mills theory – A criterion for testing the confinement models –

2018 ◽  
Vol 175 ◽  
pp. 12002
Author(s):  
Ryutaro Matsudo ◽  
Kei-Ichi Kondo ◽  
Akihiro Shibata
Keyword(s):  
Wilson Loop ◽  
String Tension ◽  
Wilson Loops ◽  
Two Dimensional ◽  
Fundamental Representation ◽  
Yang Mills ◽  
Operator Relation ◽  
Higher Dimensional ◽  
The Difference ◽  
Area Law

We examine how the average of double-winding Wilson loops depends on the number of color N in the SU(N) Yang-Mills theory. In the case where the two loops C1 and C2 are identical, we derive the exact operator relation which relates the doublewinding Wilson loop operator in the fundamental representation to that in the higher dimensional representations depending on N. By taking the average of the relation, we find that the difference-of-areas law for the area law falloff recently claimed for N = 2 is excluded for N ⩾ 3, provided that the string tension obeys the Casimir scaling for the higher representations. In the case where the two loops are distinct, we argue that the area law follows a novel law (N − 3)A1/(N − 1) + A2 with A1 and A2(A1 < A2) being the minimal areas spanned respectively by the loops C1 and C2, which is neither sum-ofareas (A1 + A2) nor difference-of-areas (A2 − A1) law when (N ⩾ 3). Indeed, this behavior can be confirmed in the two-dimensional SU(N) Yang-Mills theory exactly.

scholarly journals Lattice study of area law for double-winding Wilson loops

2018 ◽  
Vol 175 ◽  
pp. 12010
Author(s):  
Akihiro Shibata ◽  
Seikou Kato ◽  
Kei-Ichi Kondo ◽  
Ryutaro Matsudo
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Strong Coupling ◽  
Wilson Loop ◽  
Strong Coupling Expansion ◽  
Wilson Loops ◽  
Yang Mills ◽  
Lattice Monte Carlo ◽  
Area Law

We study the double-winding Wilson loops in the SU(N) Yang-Mills theory on the lattice. We discuss how the area law falloff of the double-winding Wilson loop average is modified by changing the enclosing contours C1 and C2 for various values of the number of color N. By using the strong coupling expansion, we evaluate the double-winding Wilson loop average in the lattice SU(N) Yang-Mills theory. Moreover, we compute the double-winding Wilson loop average by lattice Monte Carlo simulations for SU(2) and SU(3). We further discuss the results from the viewpoint of the Non-Abelian Stokes theorem in the higher representations.

scholarly journals Exact 1/N expansion of Wilson loop correlators in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Wolfgang Mück
Keyword(s):  
Matrix Model ◽  
Wilson Loop ◽  
Model Solution ◽  
Wilson Loops ◽  
Combinatorial Formula ◽  
Expectation Value ◽  
Yang Mills ◽  
Hooft Coupling ◽  
The Matrix ◽  
Super Yang Mills Theory

Abstract Supersymmetric circular Wilson loops in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory are discussed starting from their Gaussian matrix model representations. Previous results on the generating functions of Wilson loops are reviewed and extended to the more general case of two different loop contours, which is needed to discuss coincident loops with opposite orientations. A combinatorial formula representing the connected correlators of multiply wound Wilson loops in terms of the matrix model solution is derived. Two new results are obtained on the expectation value of the circular Wilson loop, the expansion of which into a series in 1/N and to all orders in the ’t Hooft coupling λ was derived by Drukker and Gross about twenty years ago. The connected correlators of two multiply wound Wilson loops with arbitrary winding numbers are calculated as a series in 1/N. The coefficient functions are derived not only as power series in λ, but also to all orders in λ by expressing them in terms of the coefficients of the Drukker and Gross series. This provides an efficient way to calculate the 1/N series, which can probably be generalized to higher-point correlators.

scholarly journals From Center-Vortex Ensembles to the Confining Flux Tube

Universe ◽  
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.

scholarly journals Topological Wilson-loop area law manifested using a superposition of loops

2013 ◽  
Vol 15 (4) ◽  
pp. 043041 ◽  
Author(s):  
Erez Zohar ◽  
Benni Reznik
Keyword(s):  
Wilson Loop ◽  
Loop Area ◽  
Area Law

Refinement of Water Droplets With Surfactants for Wet Compression of Gas Turbine

2009 ◽  
Author(s):  
Rongkai Zhu ◽  
Qun Zheng ◽  
Guoqiang Yue ◽  
Rakesh Bhargava
Keyword(s):  
Surface Tension ◽  
Gas Turbine ◽  
Experimental Work ◽  
Ionic Surfactants ◽  
Water Droplets ◽  
Compression Process ◽  
Surface Behavior ◽  
Wet Compression ◽  
The Cost

Concerned with the influence of the size of water droplets on the effect of wet compression, it is important to control the size of water droplets among 5–10 microns or smaller, for this purpose an experimental work is carried out by improve the surface behavior of water aiming to reduce its surface tension. Non-ionic surfactants and its combination were employed to reach such an aim. The surface tension of water was reduced from 72.9mN/m to 41.2mN/m or even lower depending on the cost. It offers a possible way to refine spray, and ready to use in wet compression process.

DOMAIN WALL NETWORK AS QCD VACUUM: CORRELATION FUNCTIONS AND CONFINEMENT OF STATIC QUARKS

2019 ◽  
pp. 38-47
Author(s):  
V.A. Tainov
Keyword(s):  
Topological Charge ◽  
Wilson Loop ◽  
Domain Model ◽  
Physical Vacuum ◽  
Qcd Vacuum ◽  
Almost Everywhere ◽  
Vacuum Fields ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Area Law

Within the domain model of QCD vacuum the properties of a statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual gluon fields representing the physical vacuum of quantum chromodynamics are investigated. The two-point correlation function of the topological charge density is calculated and the topological susceptibility is found. It is shown that such vacuum fields ensure the implementation of the area law for the Wilson loop, i.e. the confinement of static quarks.

scholarly journals Fully Quantum String Representation of a Wilson Loop in the Finite-Temperature 3D Yang–Mills Theory

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 688
Author(s):  
Dmitry Antonov
Keyword(s):  
Critical Temperature ◽  
Finite Temperature ◽  
Wilson Loop ◽  
Conformal Anomaly ◽  
Yang Mills ◽  
Quantum Description ◽  
String Representation ◽  
Confinement Phase

We demonstrate the emergence of the Polchinski–Strominger term in the string representation of a Wilson loop in the confinement phase of the finite-temperature 3D Yang–Mills theory. At a temperature which is roughly twice smaller than the deconfinement critical temperature, the value of the coupling of that term becomes such that the string conformal anomaly cancels out, thereby admitting a fully quantum description of the quark–antiquark string in 3D rather than 26D.

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