String tensions for lattice gauge theories in 2 + 1 dimensions

Compact U(1) and SU(2) lattice gauge theories in 3 euclidean dimensions are studied by standard Monte Carlo techniques. The question of extracting reliable string tensions from these theories is examined in detail, including a comparison of the Monte Carlo Wilson loop data with weak coupling predictions and a careful error analysis: our conclusions are rather different from those of previous investigations of these theories. In the case of U(1) theory, we find that only a tiny range of β values can possibly be relevant for extracting a string tension and we are unable to convincingly demonstrate the expected exponential dependence of the string tension on β. For the SU(2) theory we are able to determine, albeit with rather large errors, a string tension from a study of Wilson loops.     

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.     

Spatial string tension in <Emphasis Type="Italic">N</Emphasis><Subscript><Emphasis Type="Italic">f</Emphasis></Subscript> = 2 lattice QCD at finite temperature

The spatial string tension across a crossover from the low-temperature phase to the high-temperature phase is computed in QCD with two flavors of nonperturbatively improved Wilson fermions at small lattice spacing a ∼ 0.12 fm. We find that in the low-temperature phase spatial string tension agrees well with zero-temperature string tension. Furthermore, it does not show increasing for temperatures up to T = 1.36T _pc, the highest temperature considered. Our results agree with some theoretical predictions. The text was submitted by the authors in English.     

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).     

The spatial string tension in the deconfined phase of three-dimensional QCD in the large N limit

We numerically compute the spatial string tension in the deconfined phase of three dimensional QCD in the large N limit. Our results clearly show that the string tension grows linearly with temperature.     

Wilson loops on 324 lattices and theSU(3) potential

Wilson loops are calculated on 32⁴ lattices in the coupling regime 6/g ²=6.3–6.9. Determination of the string tension from these loops with a method based on string model calculations shows a string tension that does not seem to scale. This is probably due to the amount of statistics. It points to difficulties in obtaining accurate physical results for coupling values above 6.6. Suggestions to improve this situation are made.     

Adjoint Wilson lines and the effective gluon mass

The effective mass of the gluon is defined in terms of the energy stored in the string between adjoint sources. For SU(2) lattice gauge theory, I present Monte Carlo evidence that this mass scales correctly in the weak coupling regime and hence is non-zero and finite in the continuum limit. Various systematic errors (chief among them are temperature effects) still make it difficult to give a precise numerical value for this mass at zero temperature, but a range of 500 to 800 MeV seems reasonable (using a value for the string tension of (420 MeV)²). Some attempt is made to relate this quantity to a true “constituent gluon mass.”     

Chiral phase transition from string theory

The low energy dynamics of a certain D-brane configuration in string theory is described at weak t'Hooft coupling by a nonlocal version of the Nambu-Jona-Lasinio model. We study this system at finite temperature and strong t'Hooft coupling, using the string theory dual. We show that for sufficiently low temperatures chiral symmetry is broken, while for temperatures larger then the critical value, it gets restored. We compute the latent heat and observe that the phase transition is of the first order.     

Phase structure of four-dimensional gonihedric spin system

We perform Monte Carlo simulations of a gauge invariant spin system which describes random surfaces with gonihedric action in four dimensions. The Hamiltonian is a mixture of one-plaquette and additional two- and three-plaquette interaction terms with specially adjusted coupling constants [G.K. Savvidy, F.J. Wegner, Nucl. Phys. B 413 (1994) 605, G.K. Savvidy, K.G. Savvidy, Phys. Lett. B 324 (1994) 72] For the system with the large self-intersection coupling constant k we observe the second-order phase transition at temperature β_c - 1.75. The string tension is generated by quantum fluctuations as it was expected theoretically [G.K. Savvidy, K.G. Savvidy, Mod. Phys. Lett. A 8 (1993) 2963]. This result suggests the existence of a noncritical string in four dimensions. For smaller values of k the system undergoes the first order phase transition and for k close to zero exhibits a smooth crossover.     

Roughening transition in lattice gauge theories in arbitrary dimension: (II). The groups Z3, U(1), SU(2), SU(3)

Strong coupling expansions for the string tension and other quantities in lattice gauge theories are computed in arbitrary dimension for the groups Z₃, U(1), SU(2), SU(3). This enables us to determine the location of the roughening transition, which seems to be group independent when measured in an appropriate variable. In four dimensions, the strong coupling expansion of string tension calculated up to fourteenth order for SU(2), and twelfth order for SU(3) agrees nicely with Monte Carlo data up to the roughening point.     

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.     

The massive schwinger model on the lattice studied via a local hamiltonian Monte Carlo method

A local hamiltonian Monte Carlo method is used to study the massive Schwinger model. A non-vanishing quark condensate is found and the dependence of the condensate and the string tension on the background field is calculated. These results reproduce well the expected continuum results. We study also the first order phase transition which separates the weak and strong coupling regimes and find evidence for the behaviour conjectured by Coleman.     

Gauge string in the fermion asymmetric matter

Two new effects of interaction of the gauge string with a homogeneous density of fermions are considered in a gauge model with an anomalous coupling of vector fields with fermions. First, the presence of an induced nonzero magnetic-like helicity on the straight string is demonstrated. Second, it is shown that the equation of motion of the string is modified by a nonlinear term that can be decomposed into the correction to the string tension and an additional force perpendicular to the tangent and normal vectors of the string. Static configurations are found and their stability is studied.     

Gauge theory on a random lattice

A general formulation of gauge theory on a random lattice is developed and the strong coupling limit of the Wilson string tension worked out. The confining force found in this strong coupling limit is identical to that predicted by the relativistic string model. In particular, the force between two color-triplet charges is a constant for large separation and the tube of electric flux joining the charges fluctuates, giving it a net thickness proportional to the logarithm of its length.     

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.     

Grand canonical simulations of string tension in elastic surface model

We report a numerical evidence that the string tension σ can be viewed as an order parameter of the phase transition, which separates the smooth phase from the crumpled one, in the fluid surface model of Helfrich and Polyakov-Kleinert. The model is defined on spherical surfaces with two fixed vertices of distance L. The string tension σ is calculated by regarding the surface as a string connecting the two points. We find that the phase transition strengthens as L is increased, and that σ vanishes in the crumpled phase and non-vanishes in the smooth phase.     

Investigation of phase coupling phenomena in sustained portion of musical instruments sound

This work investigates aperiodicities that occur in the sustained portion of a sound of musical instrument played by a human player, due to synchronous versus asynchronous deviations of the partial phases. By using an additive sinusoidal analysis, phases of individual partials are precisely extracted and their correlation statistics and coupling effects are analyzed. It is shown that various musical instruments exhibit different phase coupling characteristics. The effect of phase coupling is compared to analysis by means of higher order statistics and it is shown that both methods are closely mathematically related. Following a detailed analysis of phase coupling for various musical instruments it is suggested that phase coupling is an important characteristic of a sustained portion of sound of individual musical instruments, and possibly even of instrumental families. Interesting differences in phase deviations where found for the flute, trumpet and cello. For the cello, the effect of vibrato is examined by comparing the analysis of a closed string sound played with a natural vibrato to analysis of an open string sound that contains no vibrato. Following, a possible model for phase deviations in the cello is presented and a simulation of phase fluctuations for this model is performed.     

U(3) four-dimensional lattice gauge theory and Monte Carlo calculations

Monte Carlo results for the pure U(3) lattice gauge theory on a 6⁴ lattice are reported. Wilson loops and the string tension are presented. The first-order phase transition in U(3) is reflected quite clearly in a discontinuity in the string tension at β = β_c. The U(1) factor of U(3) is extracted using the determinant of the Wilson loops. As expected, the U(1) component appears to deconfine at the phase transition..     

Pathological lattice field theory for interacting strings

A path integral expression for closed Nambu-Goto strings interacting by breaking and joining is shown to be pathological by using an equivalent euclidean lattice field theory. A class of interactions which correct this problem is discussed. Dyson-Schwinger equations are derived for string vacuum expectation values.