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.

scholarly journals Dual Superconductor Model of Confinement: Quantum-String Representation of the 4D Yang–Mills Theory on a Torus and the Correlation Length away from the London Limit

Universe ◽  
2021 ◽  
Vol 8 (1) ◽  
pp. 7
Author(s):  
Dmitry Antonov
Keyword(s):  
Partition Function ◽  
Correlation Length ◽  
Wilson Loop ◽  
Gluon Condensate ◽  
Critical Value ◽  
Low Energy ◽  
Conformal Anomaly ◽  
Energy Limit ◽  
Yang Mills ◽  
String Representation

This paper is devoted to the dual superconductor model of confinement in the 4D Yang–Mills theory. In the first part, we consider the latter theory compactified on a torus, and use the dual superconductor model in order to obtain the Polchinski–Strominger term in the string representation of a Wilson loop. For a certain realistic critical value of the product of circumferences of the compactification circles, which is expressed in terms of the gluon condensate and the vacuum correlation length, the coupling of the Polchinski–Strominger term turns out to be such that the string conformal anomaly cancels out, making the string representation fully quantum. In the second part, we use the analogy between the London limit of the dual superconductor and the low-energy limit of the 4D compact QED, to obtain the partition function of the dual superconductor model away from the London limit. There, we find a decrease of the vacuum correlation length, and derive the corresponding potential of monopole currents.

scholarly journals SHEAR VISCOSITY OF YANG–MILLS THEORY IN THE CONFINEMENT PHASE

2007 ◽  
Vol 16 (07) ◽  
pp. 1249-1260
Author(s):  
IVER BREVIK ◽  
KAZUO GHOROKU
Keyword(s):  
Critical Temperature ◽  
Cross Section ◽  
Shear Viscosity ◽  
Absorption Cross Section ◽  
Holographic Model ◽  
Absorption Cross ◽  
Yang Mills ◽  
Glueball Mass ◽  
Mills Field ◽  
Confinement Phase

In terms of a simple holographic model, we study the absorption cross-section and the shear viscosity of a pure Yang–Mills field at low temperature where the system is in the confinement phase. Then we expect that the glueball states are the dominant modes in this phase. In our holographic model, an infrared cut-off rm is introduced as a parameter which fixes the lowest mass of the glueball. As a result, the critical temperature of gluon confinement is estimated to be Tc ~ 127 MeV . For T < Tc, we find that both the absorption cross-section and the shear viscosity are independent of the temperature. Their values are frozen at the values corresponding to the critical point, for 0 < T < Tc. We discuss this behavior by considering the glueball mass and its temperature dependence.

scholarly journals STABLE CHROMOMAGNETIC QCD VACUUM AND CONFINEMENT

2010 ◽  
Vol 25 (30) ◽  
pp. 2591-2598 ◽  
Author(s):  
R. PARTHASARATHY
Keyword(s):  
Energy Density ◽  
Finite Temperature ◽  
Wilson Loop ◽  
Potential Model ◽  
Linear Potential ◽  
Effective Energy ◽  
Leading Order ◽  
Model Calculations ◽  
Yang Mills ◽  
Qcd Vacuum

The stable chromomagnetic vacuum for SU(2) Yang–Mills theory found earlier is shown to give a model for confinement in QCD, using Wilson loop and a linear potential (in the leading order) for quark–antiquark interaction. The coefficient k in this potential is found to be ~ 0.25 GeV2, in satisfactory agreement with nonrelativistic potential model calculations for charmonium. At finite temperature, the real effective energy density found earlier is used to obtain estimates of the deconfining temperature agreeing reasonably with lattice study for SU(2).

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 Quantum chaos in the Yang-Mills-Higgs system at finite temperature

2005 ◽  
Vol 42 (2) ◽  
pp. 183-190 ◽  
Author(s):  
D. U. Matrasulov ◽  
F. C. Khanna ◽  
U. R. Salomov ◽  
A. E. Santana
Keyword(s):  
Finite Temperature ◽  
Quantum Chaos ◽  
Yang Mills

SPECTRUM OF SCREENING MASSES FOR SU(2) GAUGE THEORY: UNIVERSALITY CLASS

2010 ◽  
Vol 19 (08n10) ◽  
pp. 1725-1729
Author(s):  
R. S. COSTA ◽  
S. B. DUARTE ◽  
M. CHIAPPARINI ◽  
T. MENDES
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Gauge Theory ◽  
Critical Temperature ◽  
Variational Method ◽  
Excited States ◽  
Universality Class ◽  
Yang Mills ◽  
Exponential Method ◽  
Deconfinement Phase Transition

In this work we study the spectrum of the lowest screening masses for Yang–Mills theories on the lattice. We used the SU(2) gauge group in (3 + 1) dmensions. We adopted the multiple exponential method and the so-called "variational" method, in order to detect possible excited states. The calculations were done near the critical temperature of the confinement-deconfinement phase transition. We obtained values for the ratios of the screening masses consistent with predictions from universality arguments. A Monte Carlo evolution of the screening masses in the gauge theory confirms the validity of the predictions.

Path-integral approach to anomalies at finite temperature

1990 ◽  
Vol 68 (1) ◽  
pp. 96-103 ◽  
Author(s):  
T. F. Treml
Keyword(s):  
Vector Field ◽  
Path Integral ◽  
Finite Temperature ◽  
Dimensional Regularization ◽  
Flat Space ◽  
Integral Approach ◽  
Chiral Anomaly ◽  
Conformal Anomaly ◽  
Path Integral Approach ◽  
The One

The non-Abelian chiral anomaly for a fermion interacting with an external vector field in any even dimension and the conformal anomaly, in the limit of flat space–time, for a self-interacting scalar field are shown to be independent of temperature using a simple path-integral approach that employs dimensional regularization. The chiral anomaly is used as an example to show that the methods used to study the dimensionally regularized anomaly at finite temperature are readily transferable to the case of ζ-function regularization. The conformal anomaly in (super) string theory at finite temperature is briefly discussed in the light of known results. Some subtleties concerning the use of infrared cutoffs in a dimensionally regularized approach to the computation of the one-loop effective action at finite temperature are considered in an appendix.

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