scholarly journals FINITE TEMPERATURE SU(2) GAUGE THEORY: CRITICAL COUPLING AND UNIVERSALITY CLASS

2008 ◽  
Vol 19 (07) ◽  
pp. 1079-1093 ◽  
Author(s):  
ALEXANDER VELYTSKY
Keyword(s):  
Gauge Theory ◽  
High Precision ◽  
Finite Temperature ◽  
Universality Class ◽  
String Tension ◽  
Strong Coupling Regime ◽  
Critical Coupling ◽  
Binder Cumulant ◽  
Good Agreement ◽  
3D Ising Model

We examine SU(2) gauge theory in 3 + 1 dimensions at finite temperature in the vicinity of critical point. For various lattice sizes in time direction (Nτ = 1, 2, 4, 8) we extract high precision values of the inverse critical coupling and critical values of the 4th order cumulant of Polyakov loops (Binder cumulant). We check the universality class of the theory by comparing the cumulant values to that of the 3D Ising model and find very good agreement. The Polyakov loop correlators for the indicated lattices are also measured and the string tension values extracted. The high precision values of critical coupling and string tension allow us to study the scaling of dimensionless [Formula: see text] ratio. The violation of scaling by < 10% is observed as the coupling is varied from weak to strong coupling regime.

scholarly journals Analytic Results in (2+1)-Dimensional Finite Temperature LGT

1997 ◽  
Vol 12 (32) ◽  
pp. 5753-5766 ◽  
Author(s):  
M. Billó ◽  
M. Caselle ◽  
A. D'Adda
Keyword(s):  
Monte Carlo ◽  
Effective Action ◽  
Finite Temperature ◽  
Mean Field ◽  
Polyakov Loop ◽  
Critical Coupling ◽  
Dimensional Theory ◽  
Field Techniques ◽  
Large N ◽  
Good Agreement

In a (2 + 1)-dimensional pure LGT at finite temperature the critical coupling for the deconfinement transition scales as βc(nt) = Jcnt + a1, where nt is the number of links in the "timelike" direction of the symmetric lattice. We study the effective action for the Polyakov loop obtained by neglecting the spacelike plaquettes, and we are able to compute analytically in this context the coefficient a1 for any SU(N) gauge group; the value of Jc is instead obtained from the effective action by means of (improved) mean field techniques. Both coefficients have already been calculated in the large N limit in a previous paper. The results are in very good agreement with the existing Monte Carlo simulations. This fact supports the conjecture that, in the (2 + 1)-dimensional theory, spacelike plaquettes have little influence on the dynamics of the Polyakov loops in the deconfined phase.

scholarly journals Abelian spatial string tension in finite temperature SU(2) gauge theory

2016 ◽  
Vol 31 (26) ◽  
pp. 1650149 ◽  
Author(s):  
Takashige Sekiguchi ◽  
Katsuya Ishiguro
Keyword(s):  
Gauge Theory ◽  
Critical Temperature ◽  
Dimensional Reduction ◽  
Finite Temperature ◽  
Gauge Coupling ◽  
String Tension ◽  
Lattice Volume ◽  
Volume Formula ◽  
Gauge Fixing ◽  
Error Bars

We investigate Abelian and monopole contributions to spatial string tension in the deconfined phase of finite temperature SU(2) gauge theory without imposing any gauge fixing conditions. Lattice calculations of non-Abelian and Abelian spatial string tensions from the Wilson action at gauge coupling [Formula: see text] and lattice volume [Formula: see text] [Formula: see text] show that these string tensions agree with each other within error bars at any adopted value of [Formula: see text], which implies Abelian dominance. From measurements of non-Abelian, Abelian and monopole forces that arise from the corresponding spatial string tension, furthermore, we find the tendency that the monopole contribution to the spatial string tension can be almost as large as the non-Abelian and Abelian ones. The temperature dependence of the calculated non-Abelian and Abelian spatial string tensions allows us to conclude that the concept of dimensional reduction holds both for non-Abelian and Abelian sectors at temperatures higher than twice the critical temperature.

scholarly journals Separate Universe calibration of the dependence of halo bias on cosmic web anisotropy

2020 ◽  
Vol 499 (3) ◽  
pp. 4418-4431 ◽  
Author(s):  
Sujatha Ramakrishnan ◽  
Aseem Paranjape
Keyword(s):  
Dark Matter ◽  
High Precision ◽  
Gaussian Distribution ◽  
Initial Perturbation ◽  
Analytical Framework ◽  
Web Environment ◽  
Wide Range ◽  
Galaxy Assembly ◽  
Very High ◽  
Good Agreement

ABSTRACT We use the Separate Universe technique to calibrate the dependence of linear and quadratic halo bias b1 and b2 on the local cosmic web environment of dark matter haloes. We do this by measuring the response of halo abundances at fixed mass and cosmic web tidal anisotropy α to an infinite wavelength initial perturbation. We augment our measurements with an analytical framework developed in earlier work that exploits the near-lognormal shape of the distribution of α and results in very high precision calibrations. We present convenient fitting functions for the dependence of b1 and b2 on α over a wide range of halo mass for redshifts 0 ≤ z ≤ 1. Our calibration of b2(α) is the first demonstration to date of the dependence of non-linear bias on the local web environment. Motivated by previous results that showed that α is the primary indicator of halo assembly bias for a number of halo properties beyond halo mass, we then extend our analytical framework to accommodate the dependence of b1 and b2 on any such secondary property that has, or can be monotonically transformed to have, a Gaussian distribution. We demonstrate this technique for the specific case of halo concentration, finding good agreement with previous results. Our calibrations will be useful for a variety of halo model analyses focusing on galaxy assembly bias, as well as analytical forecasts of the potential for using α as a segregating variable in multitracer analyses.

scholarly journals Effective String Description of the Confining Flux Tube at Finite Temperature

Universe ◽  
2021 ◽  
Vol 7 (6) ◽  
pp. 170
Author(s):  
Michele Caselle
Keyword(s):  
Flux Tube ◽  
Dimensional Reduction ◽  
Conformal Invariance ◽  
Finite Temperature ◽  
Gauge Theories ◽  
Linear Increase ◽  
General Introduction ◽  
Interquark Potential ◽  
Effective String Theory ◽  
Good Agreement

In this review, after a general introduction to the effective string theory (EST) description of confinement in pure gauge theories, we discuss the behaviour of EST as the temperature is increased. We show that, as the deconfinement point is approached from below, several universal features of confining gauge theories, like the ratio Tc/σ0, the linear increase of the squared width of the flux tube with the interquark distance, or the temperature dependence of the interquark potential, can be accurately predicted by the effective string. Moreover, in the vicinity of the deconfinement point the EST behaviour turns out to be in good agreement with what was predicted by conformal invariance or by dimensional reduction, thus further supporting the validity of an EST approach to confinement.

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