Hard thermal loops and the sphaleron rate on the lattice

Eprint Arxiv 1105 1931, 2011

In order to come closer to a realistic model of high-energy collisions, we simulate SU(2) lattice gauge theory under fluctuating temperature. The fluctuations are Euler-Gamma distributed, leading to a canonical state maximizing the Renyi and Tsallis entropy formulas. We test the random lattice spacing method numerically on the Polyakov Loop expectation value. The critical coupling and presumably also the critical deconfinement temperature shifts about 30 per cent to higher values with a realistic degree of fluctuations.

2005

We determine effective lattice actions for the Polyakov loop using inverse Monte Carlo techniques.

2014

We compare SU(2) Polyakov loop models with different effective actions with data from full two-color QCD simulations around and above the critical temperature. We then apply the effective theories at finite temperature and density to extract quantities like Polyakov loop correlators, effective Polyakov loop potentials and baryon density.

Physical Review D, 1985

This paper presents the results obtained by applying the t-expansion to the case of an SU(2) lattice gauge theory in 3+1-spate time dimensions. We compute the vacuum energy density, specific heat, string tension cr, mass of the lowest lying O++-glueball M and the ratio R = M2/o. Our computations converge best for the energy density, specific heat and R, and these quantities exhibit behavior which agrees with what we expect on general grounds and what is known from Euclidean Monte Carlo calculations. In particular we see a broad lump in the specific heat and determine fi to be 0 = 3.5f.2, a value which lies in the ballpark of values obtained from Monte Carlo calculations. Our direct computations of the mass of the O++ glueball and string tension cannot be easily compared to the results of Monte Carlo calculations, but appear to be consistent with what one would expect. --2 7

Nuclear Physics B, 1994

We study the three dimensional fundamental-adjoint SU(2) lattice gauge theory at finite temperature by Monte Carlo simulations. We find that the finite temperature deconfinement phase transition line joins the first order bulk phase transition line at its endpoint. Moreover, across the bulk transition line, the Polyakov loop undergoes a discontinuous jump implying the existence of both confining and deconfining phases on its two sides. Implications for universality and the nature of the confining-deconfining transition are discussed.

Physical Review D, 1993

The renormalization functions involved in the determination of the topological susceptibility in the SU(2) lattice gauge theory are extracted by direct measurements, without relying on perturbation theory. The determination exploits the phenomenon of critical slowing down to allow the separation of perturbative and non-perturbative effects. The results are in good agreement with perturbative computations.

Journal of High Energy Physics, 2007

We apply the previously proposed scheme of approximately self-consistent hard-thermal-loop resummations in the entropy of high-temperature QCD to N = 4 supersymmetric Yang-Mills (SYM) theories and compare with a (uniquely determined) R Padé approximant that interpolates accurately between the known perturbative result and the next-to-leading order strong-coupling result obtained from AdS/CFT correspondence. We find good agreement up to couplings where the entropy has dropped to about 85% of the Stefan-Boltzmann value. This is precisely the regime which in purely gluonic QCD corresponds to temperatures above 2.5 times the deconfinement temperature and for which this method of hard-thermal-loop resummation has given similar good agreement with lattice QCD results. This suggests that in this regime the entropy of both QCD and N = 4 SYM is dominated by effectively weakly coupled hard-thermal-loop quasiparticle degrees of freedom. In N = 4 SYM, strong-coupling contributions to the thermodynamic potential take over when the entropy drops below 85% of the Stefan-Boltzmann value.

Nuclear Physics B, 1996

We consider the SU(2) lattice gauge theory at finite temperature in (d+1) dimensions, with different couplings β t and β s for timelike and spacelike plaquettes. By using the character expansion of the Wilson action and performing the integrals over space-like link variables, we find an effective action for the Polyakov loops which is exact to all orders in β t and to the first nontrivial order in β s . The critical coupling for the deconfinement transition is determined in the (3+1) dimensional case, by the mean field method, for different values of the lattice size N t in the compactified time direction and of the asymmetry parameter ρ = β t /β s . We find good agreement with Montecarlo simulations in the range 1 ≤ N t ≤ 5, and good qualitative agreement in the same range with the logarithmic scaling law of QCD. Moreover the dependence of the results from the parameter ρ is in excellent agreement with previous theoretical predictions.

Nuclear Physics B, 1988

We use a new method introduced earlier to study the finite-temperature transition of SU(2) lattice gauge theory. The method is based on a direct numerical construction of the partition function of the system. The pattern of zeroes of the partition function in the complex coupling plane is used as a signal for the transition. The region of the phase transition is seen to be controlled by a pair of zeroes whose real parts are clearly resolved, and this is reflected in that the peak of the specific heat is consequently resolved into a double peak. These two peaks are then clearly seen to reflect the different contributions of plaquettes in the space-space directions of the lattice and those in the time-space directions. The finite-size scaling of the zeroes of the partition function is then used to measure the critical exponent ~ of the transition which is found to be 0.62(3).

Physics Letters B, 1998

3D electroweak sphalerons on the lattice are used as test configurations for definitions of various topological defects. In the maximally Abelian gauge they are shown to contain a symmetric array of Abelian monopoles and anti-monopoles connected by two kinds of Abelian vortex strings. Gauge-invariant lattice definitions of the Nambu monopole and the Z-vortex string are formulated which correspond to Abelian projection from the unitary gauge. The sphalerons contain in their core just one (non-Abelian) Nambu monopole-anti-monopole pair (connected by a Z-string) in an unstable saddle point bound state. This provides an example for the monopole-pair unbinding mechanism expected to work at the electroweak phase transition. The definitions of defects developed here will be used in future studies of topological aspects of this transition.