Finite-temperature gluon condensate with renormalization group flow equations (original) (raw)

The gluon condensate and the effective potential in QCD

Physics Letters B, 1990

The coefficients of the abelian part of the gluon condensate in the operator product expansion of the gluon polarisation and the ghost self-energy are calculated to lowest order in as taking into account mixing with equation of motion condensates. In this order we obtain, from the full condensate, a gauge and renormalisation group invariant contribution to the effective potential of QCD which indicates that gluon condensation accompanies asymptotic freedom.

Asymmetry of the dimension-two gluon condensate: The zero temperature case

Physical Review D, 2009

We provide an algebraic study of the local composite operators A µ A ν − δ µν d A 2 κ and A 2 µ , with d = 4 the spacetime dimension. We prove that these are separately renormalizable to all orders in the Landau gauge. This corresponds to a renormalizable decomposition of the operator A µ A ν into its trace and traceless part. We present explicit results for the relevant renormalization group functions to three loop order, accompanied with various tests of these results. We then develop a formalism to determine the zero temperature effective potential for the corresponding condensates, and recover the already known result for A 2 µ 0, together with A µ A ν − δ µν d A 2 κ = 0, a nontrivial check that the approach is consistent with Lorentz symmetry. The formalism is such that it is readily generalizable to the finite temperature case, which shall allow a future analytical study of the electric-magnetic symmetry of the A 2 µ condensate, which received strong evidence from recent lattice simulations by Chernodub and Ilgenfritz, who related their results to 3 regions in the Yang-Mills phase diagram.

A bridge between the gluon condensate and potential models

Nuclear Physics B - Proceedings Supplements, 1991

We summarize the effect of a gluon condensate for a heavy quarkonium as compared to potential models. We discuss the importance of a finite gluon correlation time which serves as a key in our understanding of a quarkonium system.

Temperature dependence of the gluon condensate and the ρ -meson mass from QCD sum rules

We determine the temperature (T ) dependence of the ρ -meson mass and the gluon condensate below the deconfinement phase transition by means of QCD sum rules. In the chiral limit we derive sum rule induced scaling relations for the vacuum parts of the Gibbs averaged scalar operators contributing to the operator product expansion of the ρ 0 current-current correlator at finite temperature. The scaling with λ ≡ s0(T )/s0(0), s0 being the T -dependent perturbative QCD continuum threshold in the spectral integral, is simple for renormalization group invariant operators, and becomes nontrivial for a set of operators which mix and scale anomalously under a change of the renormalization point. In contrast to previous works on thermal QCD sum rules with this approach the gluon condensate exhibits a sizable T -dependence which is qualitatively in accord with lattice data. The ρ -meson mass rises slowly with temperature, and there is no indication of its breakdown up to T = 160 MeV.

Gauge potential singularities and the gluon condensate at finite temperatures

Nuclear Physics B - Proceedings Supplements, 2002

The continuum limit of SU (2) lattice gauge theory is carefully investigated at zero and at finite temperatures. It is found that the continuum gauge field has singularities originating from center degrees of freedom being discovered in Landau gauge. Our numerical results show that the density of these singularities properly extrapolates to a non-vanishing continuum limit. The action density of the non-trivial Z2 links is tentatively identified with the gluon condensate. We find for temperatures larger than the deconfinement temperature that the thermal fluctuations of the embedded Z2 gauge theory result in an increase of the gluon condensate with increasing temperature.

Temperature dependence of the gluon condensate and the rho\rhorho -meson mass from QCD sum rules

2000

We determine the temperature (T) dependence of the rho\rhorho-meson mass and the gluon condensate below the deconfinement phase transition by means of QCD sum rules. In the chiral limit we derive sum rule induced scaling relations for the vacuum parts of the Gibbs averaged scalar operators contributing to the operator product expansion of the rho0\rho^0rho0 current-current correlator at finite temperature. The scaling with lambdaequivsqrts0(T)/s0(0)\lambda\equiv \sqrt{s_0(T)/s_0(0)}lambdaequivsqrts_0(T)/s0(0), s0s_0s_0 being the T-dependent perturbative QCD continuum threshold in the spectral integral, is simple for renormalization group invariant operators, and becomes nontrivial for a set of operators which mix and scale anomalously under a change of the renormalization point. In contrast to previous works on thermal QCD sum rules with this approach the gluon condensate exhibits a sizable T-dependence which is qualitatively in accord with lattice data. The rho\rhorho-meson mass rises slowly with temperature, and there is no indication of its break...

Singular gauge potentials and the gluon condensate at zero temperature

Nuclear Physics B - Proceedings Supplements, 2002

We consider a new cooling procedure which separates gluon degrees of freedom from singular center vortices in SU LGT in a gauge invariant way. Restricted by a cooling scale κ 4 /σ 2 fixing the residual SO(3) gluonic action relative to the string tension, the procedure is RG invariant. In the limit κ → 0 a pure Z(2) vortex texture is left. This minimal vortex content does not contribute to the string tension. It reproduces, however, the lowest glueball states. With an action density scaling like a 4 with β, it defines a finite contribution to the action density at T = 0 in the continuum limit. We propose to interpret this a mass dimension 4 condensate related to the gluon condensate. Similarly, this vortex texture is revealed in the Landau gauge. * Poster presented by E.-M.I. † E.-M.I. gratefully appreciates the support by the Ministry of Education, Culture and Science of Japan (Monbu-Kagaku-sho) and thanks for a CERN visitorship.

Evaporation of the gluon condensate: a model for pure gauge SU(3)c phase transition

Nuclear Physics A, 2004

We interpret lattice data for the equation of state of pure gauge SU (3) c by an evaporation model. At low temperatures gluons are frozen inside the gluon condensate, whose dynamics is described in terms of a dilaton lagrangian. Above the critical temperature quasifree gluons evaporate from the condensate: a first order transition is obtained by minimizing the thermodynamical potential of the system. Within the model it is possible to reproduce lattice QCD results at finite temperature for thermodynamical quantities such as pressure and energy. The gluonic longitudinal mass can also be evaluated; it vanishes below the critical temperature, where it shows a discontinuity. At very large temperatures we recover the perturbative scenario and gluons are the only asymptotic degrees of freedom.