Vortex free energy and string tension at strong and intermediate coupling

We present results of high temperature expansions up to order g^?24 for the vortex free energy respectively string tension in pure lattice gauge theories with gauge groups SU(2) and Z₂ in 3 and 4 dimensions. For SU(2) in 4 dimensions the result is compared with Monte Carlo calculations of Creutz and is in good agreement. An intermediate coupling region is seen, where the string tension smoothly interpolates between strong coupling and weak coupling behaviour.     

On the roughening transition in abelian lattice gauge theories

We study the width of the confining string between static quarks in abelian lattice gauge theories using strong coupling expansions. We consider gauge groups Z_n and U(1) in 3 and 4 dimensions. This extends previous work with Lüscher, where SU(2) and Z₂ were studied. In ν = 3 dimensions we find evidence for a roughening transition. It is characterized by a divergence of the string width for an infinitely far separated quark-antiquark pair, while the string tension remains non-zero. In ν = 4 dimensions for the abelian groups we do not have evidence for a roughening transition away from a phase transition.     

New issues in manifolds of SU(3) holonomy

It is shown that in compactification of superstrings on manifolds of SU(3) holonomy, the superpotential receives no string theoretic corrections from the form it takes in the field theoretic limit, at least to all finite orders in sigma model perturbation theory. Modulo nonperturbative effects, this implies that those manifolds do indeed obey the exact classical equations of superstring theory, as has been argued on other grounds. Also, it is pointed out that the superpotential — even in the field theory limit — contains terms coupling charged fields to E₆ singlets as well as self-couplings of the charged fields. A slightly tentative argument is given that on certain manifolds of SU(3) holonomy — though not all — it is possible to find conformally invariant sigma models that, while keeping unbroken supersymmetry, break E₈ to SO(10) or SU(5) rather than E₆. Including the effects of Wilson lines this would mean that E₈ could be broken precisely to SU(3) × SU(2) × U(1) while keeping unbroken supersymmetry. These facts may open avenues for solving the problems associated with neutrino masses, proton decay, and renormalization group calculations of coupling constants. They also may lead to models with fewer unknown parameters than have been present in previous quasi-realistic models.     

On the link between strong and weak coupling expansions for the SU(2) lattice gauge theory

The intermediate region between the strong and weak coupling expansions of SU(2) lattice gauge theory is analyzed by inverting the strong coupling series of the average plaquette energy E_p(J).

Taking into account the weak coupling behaviour too, we get Padé approximants for J(E_p) valid in the whole physical region. The zeros of pJ/pE_p are mapped into singularities of E_p(J); they occur for complex values of J and give rise to a peak in the specific heat in fair agreement with the Monte Carlo simulation data. The variable E_p is further used to analyze the strong coupling expansions for the roughening indicator, the string tension and the mass gap.     

Revisiting toric SU(3) structures

Three‐dimensional smooth compact toric varieties (SCTV) admit SU(3) structures, and may thus be relevant for string compactifications, if they have even first Chern class (c₁). This condition can be fulfilled by infinitely many SCTVs, including ℂℙ³ and ℂℙ¹ bundles over all two‐dimensional SCTVs. We show that as long as c₁ is even, toric SU(3) structures can be constructed using a method proposed in [1]. We perform a systematic study of the parametric freedom of the resulting SU(3) structures, with a particular focus on the metric and the torsion classes. Although metric positivity constrains the SU(3) parameters, we find that every SCTV admits several toric SU( 3) structures and that parametric choices can sometimes be made to match requirements of string vacua. We also provide a short review on the constraints that an SU(3) structure must meet to be relevant for four‐dimensional, maximally symmetric �� = 1 or �� = 0 string vacua.     

High-temperature expansions for the free energy of vortices and the string tension in lattice gauge theories

We derive high-temperature cluster expansions for the free energy of vortices in SU(2) and Z₂ lattice gauge theories in 3 and 4 dimensions. The expected behaviour of the vortex free energy is verified. It obeys an area law behaviour. The coefficient of the area is shown to be equal to the string tension between static quarks. We calculate its expansion up to 12th order. For SU(2) in 4 dimensions the result is compared with Monte Carlo calculations of Creutz and is in good agreement at strong and intermediate coupling.     

Thermodynamics of SU(3) lattice gauge theory

The pressure and the energy density of the SU(3) gauge theory are calculated on lattices with temporal extent N_τ = 4, 6 and 8 and spatial extent N_σ = 16 and 32. The results are then extrapolated to the continuum limit. In the investigated temperature range up to five times T_c we observe a 15% deviation from the ideal gas limit. We also present new results for the critical temperature on lattices with temporal extent N_τ = 8 and 12. At the corresponding critical couplings the string tension is calculated on 32⁴ lattices to fix the temperature scale. An extrapolation to the continuum limit yields T_c/√σ = 0.629(3). We furthermore present results on the electric and magnetic condensates as well as the temperature dependence of the spatial string tension. These observables suggest that the temperature dependent running coupling remains large even at T ≅ 5T_c. For the spatial string tension we find √σ_s/T=0.566(13)g²2(T) with g² (5T_c) ≅ 1.5.     

SU(2) Lattice gauge theory in (2+1)D

Cluster expansion methods are applied to theSU(2) lattice gauge model in (2+1) dimensions. Strong-coupling series are calculated for the vacuum energy per site, the axial string tension, and the scalar mass gap; while ELCE approximants are used to estimate the string tension beyond its roughening transition. The simple scaling behaviour expected of this super-renormalizable theory is clearly seen, and we estimate that in the continuum limit the string tension σ～(0.14±0.01)g ⁴, while the mass gapM _s ～(2.2±0.25)g ². More accurate Monte Carlo simulations are needed to check the universality between the Hamiltonian and Euclidean versions of this model.     

Generalized roughening transition and its effect on the string tension

The well-understood roughening transition of an interface in the d = 3 Ising model implies an essential singularity in the string tension of the dual Z₂ gauge model. The roughening transition corresponds to the delocalization of the string due to strong long-wavelength fluctuations, and this reformulation can be generalized to other gauge groups and to d = 4 also. It is not a deconfining transition - it is expected to occur deep in the confining region - but its presence would raise serious questions about the continuation of strong coupling expansions of the tension beyond this point. In this paper predictions on the roughening transition are confronted with the available information on the string tension for different gauge groups in three dimensions.     

Linked cluster expansions for U(1) lattice gauge theory in 2 + 1 and 3 + 1 dimensions

Compact U(1) lattice gauge theory is studied in 2 + 1 and 3 + 1 dimensions using strong coupling series expansions and the recently proposed exact linled cluster expansion alborithm Results for the vacuum energy, specific heat and axial string tension in 2 + 1 dimensions are in agreement with previous finite lattice estimates. In 3 + 1 dimensions, we present new strong coupling series results (order g^?40) which together with the ELCE estimates show evidence of a continuous phase transition at x = 1/g⁴ = 0.72 ± 0.08. The associated critical index for the vanishing string tension is μ = 0.65 ± 0.12. The axial string tension in D = 3 + 1 appears to undergo a non-deconfining roughening transition at smaller x (0.56 ± 0.07).     

Stochastic confinement and dimensional reduction (II). Three-dimensional SU(2) lattice gauge theory

We study 3-dimensional SU(2) lattice gauge theory with respect to dimensional reduction. By Monte Carlo calculations we find that this reduction is valid to a good approximation (within ≈10%). The adjoint string tension is found to scale approximately. We also compare the adjoint string tension with a string theory.     

Monte-Carlo calculations of some quantities in SU(2) lattice gauge theory

Monte-Carlo calculations of the order parameter and the string tension in SU(2) lattice gauge theory are performed. The parameterization of the group elements of SU(2) used in our contribution differs from the standard one. The comparison with papers using standard parametrization is given and the obtained results are discussed.     

't Hooft loop in SU(2) Yang-Mills theory

We study the behavior of the spatial and temporal 't Hooft loop at zero and finite temperature in the 4D SU(2) Yang-Mills theory, using a new numerical method. In the deconfined phase T > T(c), the spatial 't Hooft loop exhibits a dual string tension, which vanishes at T(c) with a 3D Ising-like critical exponent.     

Three-Quark Potential in SU(3) Lattice QCD

The static three-quark ( 3Q) potential is studied in SU(3) lattice QCD with 12(3)x24 and beta = 5.7 at the quenched level. From the 3Q Wilson loop, 3Q ground-state potential V(3Q) is extracted using the smearing technique for ground-state enhancement. With accuracy better than a few percent, V(3Q) is well described by a sum of a constant, the two-body Coulomb term, and the three-body linear confinement term sigma(3Q)L(min), with L(min) the minimal value of total length of color flux tubes linking the three quarks. Comparing with the Q-&Qmacr; potential, we find a universal feature of the string tension, sigma(3Q) approximately sigma(Q&Qmacr;), and the OGE result for Coulomb coefficients, A(3Q) approximately 1 / 2A(Q&Qmacr;).     

How well do Monte Carlo simulations distinguish between U(1) and SU(2)?: A study of the string tension in U(1) lattice gauge theory

To investigate how a system with a known deconfining phase transition behaves when studied on finite lattices via Monte Carlo simulations, we have made such studies of compact U(1) lattice gauge theory for 8⁴, 10⁴, and 12⁴ lattices. We have concentrated on the mean plaquette energy and the string tension. The string tension does not vanish on a finite lattice, but using finite size scaling arguments the indications are that it does vanish on an infinite lattice, where we predict the critical coupling β_c = 1.008 and the correlation length exponent $\text{ν =}\text{1}\text{3}$. We compare our results to those for SU(2) and find that although there are differences, they are not yet definitive.     

Composite solitons in SU(3) spin–orbit-coupling Bose gases

We study solitons in a spin-1 Bose–Einstein condensates with SU(3) spin–orbit coupling. We obtain the ground state and the metastable solution for solitons with attractive interactions by the imaginary-time evolution method. Compared with the SU(2) spin–orbit coupling, it is found that the solitons in SU(3) spin–orbit coupling show a new feature due to breaking the symmetry. The solitons called the composite solitons have mixing manifolds of ferromagnetic and antiferromagnetic states. This has stimulated people to study the topological excitation properties of SU(3) spin–orbit coupling and it is expected to find new quantum phases.     

Strong coupling series for glueball masses in (2+1) dimensional PQED

We compute glueball masses to high order in strong coupling perturbation theory, and find no evidence for pathologies of the kind observed for the tension of the string (roughening). Results suggest a smooth extrapolation of the mass gap to the weak coupling regime.     

Superconductivity in Restricted Chromo-Dynamics (RCD) in SU(2) and SU(3) Gauge Theories

Characterizing the dyonically condensed vacuum by the presence of two massive modes (one determining how fast the perturbative vacuum around a colour source reaches the condensation and the other giving the penetration length of colored flux) in SU(2) theory, it has been shown that due to the dynamical breaking of magnetic symmetry the vacuum of RCD acquires the properties similar to those of relativistic superconductor. Analysing the behaviour of dyons around RCD string, the solutions of classical field equations have been obtained and it has been shown that magnetic constituent of dyonic current is zero at centre of the string and also at the points far away from the string. Extending RCD in the realistic color gauge group SU(3), it has been shown that the resulting Lagrangian leads to dyonic condensation, color confinement and the superconductivity with the presence of two scalar modes and two vector modes.     

SU (2) lattice gauge theory and Monte Carlo calculations

Monte Carlo results for theSU (2) lattice gauge theory in four dimensions are presented. The string tension is measured with high statistics and also the mass of the perimeter term is determined. Wilson loop-plaquette correlations, which are related to roughening, are measured.     

SU(3) symmetry for the vector meson-nucleon interaction

When comparing data on VBB coupling constants with SU(3) one usually assumes Sakurai's idea that the ?-meson couples universally to the isovector current. In order to use this assumption one has to continue the coupling from the vector meson pole to t=0. The implications for the coupling constants depend upon how this continuation is carried out. In this paper we present arguments to expect simple continuation properties for VNN form factors defined in analogy with the Sachs electromagnetic form factors, rather than for the vector and tensor form factors. We show that in this case experimental data are consistent with SU(3), Sakurai's universality idea and with Zweig's rule. Furthermore we find $\text{F}\text{D}$ ratios close to the SU(6) prediction.