Yang-Mills Thermodynamics Research Articles

SU(2) Quantum Yang–Mills Thermodynamics: Some Theory and Some Applications

In the first part of this talk, we review some prerequisites for and essential arguments involved in the construction of the thermal-ground-state estimate underlying the deconfining phase in the thermodynamics of SU(2) Quantum Yang–Mills theory and how this structure supports its distinct excitations. The second part applies deconfining SU(2) Yang–Mills thermodynamics to the Cosmic Microwave Background in view of (i) a modified temperature-redshift relation with an interesting link to correlation-length criticality in the 3D Ising model, (ii) the implied minimal changes in the dark sector of the cosmological model, and (iii) best-fit parameter values of this model when confronted with the spectra of the angular two-point functions temperature-temperature (TT), temperature-E-mode-polarisation (TE), E-mode-polarisation-E-mode-polarisation (EE), excluding the low-l physics. The latter, which so far is treated in an incomplete way due to the omission of radiative effects, is addressed in passing.

SU(2)cmband the cosmological model: angular power spectra

Driven by the CMB temperature-redshift ($T$-$z$) relation as demanded by deconfining SU(2) Yang-Mills thermodynamics, an according cosmological model is proposed and analysed. This model -- SU(2)$_\CMB$ -- exhibits a dark sector, representing $\Lambda$CDM with a certain late-time dark-matter density which transitions to a reduced (present-day) density parameter at high $z$. We statistically analyse constraints on cosmological parameters directly imposed by the values of the standard co-moving ruler $r_d$ and the angular size of the sound horizon $\theta_*$. Compared to the $\Lambda$CDM best fit to 2015 Planck data, we require an increased (present-day) dark matter density when $r_d\cdot H_0=$\,const and a value $H_0\sim 73.5$ km\,s$^{-1}$Mpc$^{-1}$ -- typical for local extractions -- are used. The ratio between the density parameters of primordial and late-time dark matter ranges between 0.5 and 0.7. We confirm this trend by fitting the predictions of SU(2)$_\CMB$, obtained from a modified CLASS code, to the angular power spectra TT, TE, and EE. We consider adiabatic, scalar primordial curvature perturbations and distinguish two treatments of thermal quasi-particles in the perturbation equations. Best fits predict a red-tilted primordial power spectrum. Moreover, a low baryon density is obtained compared with the coincidence value of BBN, the $\Lambda$CDM best fit of the 2015 Planck data, and the observed deuterium abundance. Our derived values of $H_0$ support the results of local cosmological observations. Also, there is a tendency for late reionisation.

SU(2) Yang-Mills thermodynamics: A priori estimate and radiative corrections

We review and explain essential characteristics of the a priori estimate of the thermal ground state and its excitations in the deconfining phase of SU(2) Quantum Yang-Mills thermodynamics. This includes the spatially central and peripheral structure of Harrington-Shepard (anti)calorons, a sketch on how a spatial coarse-graining over (anti)caloron centers yields an inert scalar field, which is responsible for an adjoint Higgs mechanism, the identification of (anti)caloron action with ħ, a discussion of how, owing to (anti)caloron structure, the thermal ground state can be excited (wave-like and particlelike massless modes, massive thermal quasiparticle fluctuations), the principle role of and accounting for radiative corrections, the exclusion of energy-sign combinations due to constraints on momenta transfers in four-vertices in a completely fixed, physical gauge, dihedral diagrams and their resummation up to infinite loop order in the massive sector, and the resummation of the one-loop polarisation tensor of the massless modes. We also outline applications of deconfining SU(2) Yang-Mills thermodynamics to the Cosmic Microwave Background (CMB) which affect the cosmological model at high redshifts, the redshift for re-ionization of the Universe, the CMB angular power spectra at low l, and the late-time emergence of intergalactic magnetic fields.

The Isolated Electron: De Broglie’s Hidden Thermodynamics, SU(2) Quantum Yang-Mills Theory, and a Strongly Perturbed BPS Monopole

Based on a recent numerical simulation of the temporal evolution of a spherically perturbed BPS monopole, SU(2) Yang-Mills thermodynamics, Louis de Broglie’s deliberations on the disparate Lorentz transformations of the frequency of an internal “clock” on one hand and the associated quantum energy on the other hand, and postulating that the electron is represented by a figure-eight shaped, self-intersecting center vortex loop in SU(2) Quantum Yang-Mills theory we estimate the spatial radius R 0 of this self-intersection region in terms of the electron’s Compton wave length λ C . This region, which is immersed into the confining phase, constitutes a blob of deconfining phase of temperature T 0 mildly above the critical temperature T c carrying a frequently perturbed BPS monopole (with a magnetic-electric dual interpretation of its charge w.r.t. U(1)⊂SU(2)). We also establish a quantitative relation between rest mass m 0 of the electron and SU(2) Yang-Mills scale Λ , which in turn is defined via T c . Surprisingly, R 0 turns out to be comparable to the Bohr radius while the core size of the monopole matches λ C , and the correction to the mass of the electron due to Coulomb energy is about 2%.

Massive loops in thermal SU(2) Yang–Mills theory: Radiative corrections to the pressure beyond two loops

We address the loop expansion of the pressure in the deconfining phase of SU(2) Yang–Mills thermodynamics. We devise an efficient book-keeping of excluded energy-sign and scattering-channel combinations for the loop four-momenta associated with massive quasiparticles, circulating in (connected) bubble diagrams subject to vertex constraints inherited from the thermal ground state. These radiative corrections modify the one-loop pressure exerted by free thermal quasiparticles. Increasing the loop order in two-particle irreducible (2PI) bubble diagrams, we exemplarily demonstrate a suppressing effect of the vertex constraints on the number of valid combinations. This increasingly strong suppression gave rise to the conjecture in arXiv:hep-th/0609033 that the loop expansion would terminate at a finite order. Albeit the low-temperature dependence of the 2PI 3-loop diagram complies with this behavior, a thorough analysis of the high-temperature situation reveals that the leading power in temperature is thirteen such that this diagram dominates all lower loop orders for sufficiently high temperatures. An all-loop-order resummation of 2PI diagrams with dihedral symmetry is thus required, defining an extremely well-bounded analytical continuation of the low-temperature result.

SU(2)CMB at high redshifts and the value of H0

We investigate a high-$z$ cosmological model to compute the co-moving sound horizon $r_s$ at baryon-velocity freeze-out towards the end of hydrogen recombination. This model assumes a replacement of the conventional CMB photon gas by deconfining SU(2) Yang-Mills thermodynamics, three flavours of massless neutrinos ($N_\nu=3$), and a {\sl purely baryonic} matter sector (no cold dark-matter (CDM)). The according SU(2) temperature-redshift relation of the CMB is contrasted with recent measurements appealing to the thermal Sunyaev-Zel'dovich effect and CMB-photon absorption by molecular rotations bands or atomic hyperfine levels. Relying on a realistic simulation of the ionization history throughout recombination, we obtain $z_*=1693.55\pm 6.98$ and $z_{\rm drag}=1812.66\pm 7.01$. Due to considerable widths of the visibility functions in the solutions to the associated Boltzmann hierarchy and Euler equation we conclude that $z_*$ and $z_{\rm drag}$ over-estimate the redshifts for the respective photon and baryon-velocity freeze-out. Realistic decoupling values turn out to be $z_{{\rm lf},*}=1554.89\pm 5.18$ and $z_{\rm lf,drag}=1659.30\pm 5.48$. With $r_s(z_{\rm lf,drag})=(137.19\pm 0.45)\,$Mpc and the essentially model independent extraction of $r_s\cdot H_0=\mbox{const}$ from low-$z$ data in arXiv:1607.05617 we obtain a good match with the value $H_0=(73.24\pm 1.74)\,$km\,s$^{-1}$\,Mpc$^{-1}$ extracted in arXiv:1604.01424 by appealing to Cepheid calibrated SNe~Ia, new parallax measurements, stronger constraints on the Hubble flow, and a refined computation of distance to NGC4258 from maser data. We briefly comment on a possible interpolation of our high-$z$ model, invoking percolated and unpercolated U(1) topological solitons of a Planck-scale axion field, to the phenomenologically successful low-$z$ $\Lambda$CDM cosmology.

Polyakov loop and gluon quasiparticles: A self-consistent approach to Yang–Mills thermodynamics

We present a quasiparticle model for the pure gauge sector of QCD, in which transverse quasigluons propagate in a Polyakov loop background field. By incorporating thermodynamic self-consistency in the approach, we show that our Polyakov loop extended quasiparticle model allows an accurate description of recent lattice results for all the thermodynamic quantities, including the Polyakov loop expectation value, in the deconfined phase. The related quasigluon mass exhibits a distinct temperature dependence, which is connected with the non-perturbative behavior seen in the scaled interaction measure of the pure gauge theory.

Interplay between chromoelectric and chromomagnetic gluons in Yang-Mills thermodynamics

We propose an effective theory of SU(3) gluonic matter where interactions between color-electric and color-magnetic gluons are constrained by the center and scale symmetries. Through matching to the dimensionally-reduced magnetic theories, the magnetic gluon condensate qualitatively changes its thermal behavior above the critical temperature. We argue its phenomenological consequences for the thermodynamics, in particular the dynamical breaking of scale invariance.

Charge-Density Waves in Deconfining SU(2) Yang-Mills Thermodynamics

At one-loop accuracy we compute, characterize, and discuss the dispersion laws for the three low-momentum branches of propagating longitudinal, electric U(1) fields in the effective theory for the deconfining phase of pure SU(2) Yang-Mills thermodynamics. With an electric-magnetically dual interpretation of SU(2)$_{\tiny CMB}$ we argue that upon a breaking of plasma isotropy and homogeneity, introduced e.g. by a temperature gradient, the longitudinal modes could conspire to provide magnetic seed fields for magneto-hydrodynamical dynamos inside structures of galaxy, galaxy-cluster, and cosmological scales. Such a scenario ultimately links structure with seed-field formation. As judged from the present cosmological epoch, the maximally available coherent field strength of 10$^{-8}$\,Gauss from SU(2)$_{\tiny CMB}$ matches with the upper bound for cosmological present-day field strength derived from small-angle anisotropies of the cosmic microwave background.

Effective gluon potential and hybrid approach to Yang-Mills thermodynamics

We derive the partition function for the SU(3) Yang-Mills theory in the presence of a uniform gluon field within the background field method. We show, that the $n$-body gluon contributions in the partition function are characterized solely by the Polyakov loop. We express the effective action through characters of different representations of the color gauge group resulting in a form deduced in the strong-coupling expansion. A striking feature of this potential is that at low temperature gluons are physically disfavored and therefore they do not yield the correct thermodynamics. We suggest a hybrid approach to Yang-Mills thermodynamics, combining the effective gluon potential with glueballs implemented as dilaton fields.

The Quantum of Action and Finiteness of Radiative Corrections: Deconfining SU(2) Yang-Mills Thermodynamics

The quantum of action $\hbar$, multiplying in certain powers perturbative vertices in 4D gauge theory, is related to the action of just-not-resolved selfdual and thermal gauge field configurations, calorons and anticalorons, of charge modulus unity. Appealing to the derivation of the effective theory for the deconfining phase of SU(2) Yang-Mills thermodynamics, we conclude that these vertex inducers convey a rapidly decreasing interaction strength between {\sl fundamental} plane waves when the momentum transfer is increased away from the scale of maximal, {\sl effective} resolution. This adds a deeper justification to the renormalization programme of perturbation theory which ignores the contribution to the partition function of nontrivially selfdual configurations. We also point out a connection between the QED fine-structure constant $\alpha$ and the electric-magnetically dual of the effective gauge coupling in the deconfining phase, and we illustrate the workings of effective loops in the expansion of the pressure.

Onset of Magnetic Monopole-Antimonopole Condensation

We determine the critical strength of the effective electric coupling for the onset of Bose condensation of stable magnetic monopoles and antimonopoles in SU(2) Yang-Mills thermodynamics. Two scenarios are considered: infinitely fast and infinitely slow downward approaches of the critical temperature. Our results support the claim that the first lepton family and the weak interactions emerge from pure SU(2) gauge dynamics of scale MeV.

Charged Lepton Spectra from Hot-Spot Evaporation

Spectra for the emission of charged leptons from evaporating hot-spots of preconfining phase in SU(2) Yang-Mills thermodynamics are computed. Specifically, we consider charged single and dileptons with their spectra being functions of energy and invariant mass, respectively. In the former case, our results relate to narrow and correlated electron and positron peaks measured in supercritical heavy-ion collisions performed at GSI in the 1980s. In the latter case, we point out how strongly the spectra depend on typical kinematic cuts (CDF analysis of Tevatron Run II data). We also propose a scenario on how muon events of anomalously high multiplicity and large impact-parameter modulus arise in the Tevatron data.

Loop Expansion in Yang–Mills Thermodynamics

We argue that a selfconsistent spatial coarse-graining, which involves interacting (anti)calorons of unit topological charge modulus, implies that real-time loop expansions of thermodynamical quantities in the deconfining phase of SU(2) and SU(3) Yang-Mills thermodynamics are, modulo 1PI resummations, determined by a finite number of connected bubble diagrams.

Comments on Yang–Mills thermodynamics: The Hagedorn spectrum and the gluon gas pictures for a generic gauge algebra

We discuss the dependence of pure Yang–Mills equation of state on the choice of gauge algebra. In the confined phase, we generalize to an arbitrary simple gauge algebra Meyerʼs proposal of modeling the Yang–Mills matter by an ideal glueball gas in which the high-lying glueball spectrum is approximated by a Hagedorn spectrum of closed-bosonic-string type. Such a formalism is undefined above the Hagedorn temperature, corresponding to the phase transition toward a deconfined state of matter in which gluons are the relevant degrees of freedom. Under the assumption that the renormalization scale of the running coupling is gauge-algebra independent, we discuss about how the behavior of thermodynamical quantities such as the trace anomaly should depend on the gauge algebra in both the confined and deconfined phase. The obtained results compare favorably with recent and accurate lattice data in the su(3) case and support the idea that the more the gauge algebra has generators, the more the phase transition is of first-order type.

CORRELATION OF ENERGY DENSITY IN DECONFINING SU(2) YANG–MILLS THERMODYNAMICS

We compute the two-point correlation of the energy density for the massless mode in deconfining SU(2) Yang–Mills thermodynamics and point towards a possible application for the physics of cold, dilute, and stable clouds of atomic hydrogen within the Milky Way.

YANG–MILLS THERMODYNAMICS AT LOW TEMPERATURE

For the confining phase of SU(2) Yang–Mills thermodynamics, we show that the asymptotic series representing the pressure is Borel summable for negative (unphysical) values of a suitably defined coupling constant. The inverse Borel transform is meromorphic except for a branch cut along the positive-real axis. The physical pressure is precisely nil at vanishing and acquires a small imaginary admixture at small temperature, the latter indicating violations of thermal equilibrium (turbulences).

Linear growth of the trace anomaly in Yang-Mills thermodynamics

In the lattice work by Miller and in the work by Zwanziger a linear growth of the trace anomaly for high temperatures was found in pure SU(2) and SU(3) Yang-Mills theories. While future numerical work is needed to confirm or to rule out the linear growth, the aforementioned results point to the remarkable property that the corresponding systems are strongly interacting even at high temperatures. We show that within an analytical approach to Yang-Mills thermodynamics this linear rise is obtained and is directly connected to the presence of a temperature-dependent ground state, which describes (part of) the nonperturbative nature of the Yang-Mills system. Our predictions are in approximate agreement with Miller and Zwanziger.

IRREDUCIBLE THREE-LOOP CONTRIBUTIONS TO THE PRESSURE IN YANG–MILLS THERMODYNAMICS

In the effective theory for the deconfining phase of SU(2) Yang–Mills thermodynamics we compute estimates for the moduli of the irreducible three-loop diagrams contributing to the pressure. Our numerical results are in agreement with general expectations.

ERRATA: "SU(2) AND SU(3) YANG–MILLS THERMODYNAMICS AND SOME IMPLICATIONS"

We sketch the development of effective theories for SU(2) and SU(3) Yang-Mills thermodynamics. The most important results are quoted and some implications for particle physics and cosmology are discussed.