Finite size Wilson loops

A study of Wilson loop averages for finite size loops is initiated. Within the framework of euclidean four-dimensional lattice SU(2) gauge theory with elementary Wilson action we compute the expectation values of all rectangular loops to 12th order in the strong coupling expansion. The leading term for weak coupling is evaluated for loops up to 4 × 4. A comparison to Monte Carlo data is presented. Other related issues are also discussed.     

Some predictions for an improved fermion action on the lattice

We propose an improved fermion action on the lattice by adding a next nearest neightbor interaction term to Wilson action. The proposed action is expected to approach the continuum limit more rapidly. Using the improved action, the predictions for the critical value of the hopping parameter at weak and strong coupling are given. The relationship between quark masses on the lattice and in the continuum is also discussed.     

Strong coupling expansion for the mass gap in SU(2) lattice gauge theory with mixed action

We perform a strong coupling expansion up to O(β⁷) for the mass-gap in SU(2) lattice gauge theory with mixed action. A novel feature of the strong coupling expansion is discussed. The strong coupling series appears to approach the scaling region more smoothly and Padé approximants become more stable than in the case with simple Wilson action. The region of validity of a recently proposed resummation of perturbation theory as applied to the determination of the asymptotic scaling behavior is investigated. Results of a strong coupling calculation for the heat kernel action, which is related to the mixed action for a special choice of parameters, are also reported.     

Numerical simulations with two flavours of twisted-mass Wilson quarks and DBW2 gauge action

Discretisation errors in two-flavour lattice QCD with Wilson quarks and DBW2 gauge action are investigated by comparing numerical simulation data at two values of the bare gauge coupling. Both non-zero- and zero-twisted-mass values are considered. The results, including also data from simulations using the Wilson plaquette gauge action, are compared to next-to-leading order chiral perturbation theory formulas.     

Direct evidence for a Coulombic phase in monopole-suppressed SU(2) lattice gauge theory

Further evidence is presented for the existence of a non-confining phase at weak coupling in SU(2) lattice gauge theory. Using Monte Carlo simulations with the standard Wilson action, gauge-invariant SO(3)–Z2 monopoles, which are strong-coupling lattice artifacts, have been seen to undergo a percolation transition exactly at the phase transition previously seen using Coulomb gauge methods, with an infinite lattice critical point near β=3.2$\beta =3.2$. The theory with both Z2 vortices and monopoles and SO(3)–Z2 monopoles eliminated is simulated in the strong-coupling (β=0$\beta =0$) limit on lattices up to 60⁴. Here, as in the high-β phase of the Wilson-action theory, finite size scaling shows it spontaneously breaks the remnant symmetry left over after Coulomb gauge fixing. Such a symmetry breaking precludes the potential from having a linear term. The monopole restriction appears to prevent the transition to a confining phase at any β  . Direct measurement of the instantaneous Coulomb potential shows a Coulombic form with moderately running coupling possibly approaching an infrared fixed point of α∼1.4$\alpha \sim 1.4$. The Coulomb potential is measured to 50 lattice spacings and 2 fm. A short-distance fit to the 2-loop perturbative potential is used to set the scale. High precision at such long distances is made possible through the use of open boundary conditions, which was previously found to cut random and systematic errors of the Coulomb gauge fixing procedure dramatically. The Coulomb potential agrees with the gauge-invariant interquark potential measured with smeared Wilson loops on periodic lattices as far as the latter can be practically measured with similar statistics data.     

Variational Cumulant Expansion Study of Z(N) Lattice Gauge Theory with Symanzik's Improved Action

With the variational cumulant expansion (VCE) method, the internal energy and the specific heat of the Z(N) lattice gauge theory with Symanzik's improved action are calculated up to the third order. The variational parameter is determined by the main valued method and the result is compared with the VCE result for standard Wilson action. Furthermore, the changes are compared with those of the SU(2) case.     

Transfer Matrices and Lattice Fermions at Finite Density

I discuss the connection between the Hamiltonian and path integral approaches for fermionic fields. I show how the temporal Wilson projection operators appear naturally in a lattice action. I also carefully treat the insertion of a chemical potential term.     

Convergence of U(1)3 lattice gauge theory to its continuum limit

It is shown that in three space-time dimensions the pure U(1) lattice gauge theory with Villain action and fixed coupling constant converges to the free electromagnetic field as the lattice spacing approaches zero. The same holds for the Wilson action on the electric sector.     

Configuration vibronic mixing for a neutral vacancy in silicon and diamond

Configuration vibronic mixing is considered for a fully symmetric Jahn-Teller electronic term with orientation-degenerate terms (due to the distortion direction) including a correlation correction in a single-open-shell approximation. The approach is nonempirical and involves only linear vibronic coupling. The adiabatic potential is a multiwell one, because the different configurations involved in the exact Jahn-Teller term have different vibronic coupling with a lattice distortion. The stabilization energy, the frequencies of local lattice vibrations, the vibronic coupling parameter, and the energy barriers to migration and to distortion-axis reorientation are estimated for a neutral vacancy in silicon and diamond with allowance made for configuration vibronic coupling. The estimates agree with the results obtained by different experimental and theoretical methods for a wide range of properties associated with the Jahn-Teller effect.     

Portraits of the flux tube in QED3: A Monte Carlo simulation with external sources

We determine numerically, and display graphically, the electromagnetic energy distribution due to static sources in compact QED₃. Using the polymer formulation of the functional integral, Monte Carlo simulations are performed with external sources included in the lattice action. Both the Wilson and Villain forms of the action are studied, and the string tension is determined in a small range of weak couplings. For the Villain action, our values for the string tension σ are in agreement with Polyakov's formula. For the Wilson action, we are able to detect a string tension in a range of weak couplings 2.1 ? β ? 2.3 below the weak-to-strong coupling cross-over point. In the same range, standard Monte Carlo results for up to 8 × 8 Wilson loops are consistent with ordinary perturation theory (no confinement). A possible explanation of this discrepancy is discussed, and it is suggested that the standard (source-free) Monte Carlo might miss configurations which are important for flux-tube formation.     

Chiral and conformal anomalies in lattice gauge theory

The continuum limit of the chiral and conformal (Weyl) Ward-Takahashi identities in the lattice Wilson action is studied. The Wilson term works for the chiral anomaly, but it gives rise to-15 times the conventional conformal anomaly for a smallr-parameter and a very sensitiver-dependence of the Λ-parameter. This shows that the strong symmetry breaking by the Wilson term by itself does not necessarily generate correct anomalies. In the lattice regularization the functional Jacobian factors becomec-numbers and do not contribute to anomalies, corresponding to the cut-off of short distance components; the naive continuum limit of lattice WT identities can thus behave differently from continuum ones. To reconstruct conventional identities from lattice relations, the lattice composite operators should be rewritten in terms of relevant continuum operators. In general, this identification of relevant operators is facilitated either by the procedure corresponding to Zimmermann's normal product algorithm or simply by the use of auxiliary regulators such as the dimensional regulator.     

Lattice simulation of a center symmetric three-dimensional effective theory for SU(2) Yang-Mills

We perform simulations of an effective theory of SU(2) Wilson lines in three dimensions. Our action includes a kinetic term, the one-loop perturbative potential for the Wilson line, a non-perturbative “fuzzy-bag” contribution and spatial gauge fields. We determine the phase diagram of the theory and confirm that, at moderately weak coupling, the non-perturbative term leads to eigenvalue repulsion in a finite region above the deconfining phase transition.     

The sigma-model with Wilson lattice fermions

The σ-model with Wilson fermions is considered in one-loop lattice perturbation theory and in the hopping-parameter expansion at large bare couplings. Chiral-symmetry restoration in the large cut-off limit of perturbation theory is only possible if asymmetric counterterms are added to the lattice action. In the hopping-parameter expansion at infinitely large bare Yukawa coupling, dynamical parity doubling of the fermion occurs.     

The action of SU(N) lattice gauge theory in terms of the heat kernel on the group manifold

We consider the heat kernel on the group manifold as an alternative to the Wilson action in lattice gauge theory, and we exhibit its strict analogy with the well-known Berezinski-Villain action. With the heat kernel action, the Gross-Witten singularity is rigorously absent in two dimensions. The similarity of the heat kernel action to the hamiltonian approach should provide a better convergence of the lagrangian strong coupling expansion, while its behaviour at weak coupling should simplify the analysis of the weak coupling perturbative expansion.     

The phase structure of lattice QCD with two flavors of Wilson quarks and renormalization group improved gluons

The effect of changing the lattice action for the gluon field on the recently observed [F. Farchioni, R. Frezzotti, K. Jansen, I. Montvay, G.C. Rossi, E. Scholz, A. Shindler, N. Ukita, C. Urbach, I. Wetzorke, Eur. Phys. J. C 39, 421 (2005); hep-lat/0406039] first order phase transition near zero quark mass is investigated by replacing the Wilson plaquette action by the DBW2 action. The lattice action for quarks is unchanged: it is in both cases the original Wilson action. It turns out that Wilson fermions with the DBW2 gauge action have a phase structure where the minimal pion mass and the jump of the average plaquette are decreased, when compared to Wilson fermions with Wilson plaquette action at similar values of the lattice spacing. Taking the DBW2 gauge action is advantageous also from the point of view of the computational costs of numerical simulations.Received: 29 October 2004, Revised: 7 March 2005, Published online: 31 May 2005     

Phonon or electron friction of a quantum heavy particle

Summary In this paper we analyse, with the path integral method, the diffusion of a quantum heavy particle moving in a strongly corrugated periodic potential both in the case when the particle is interacting with a thermal bath of phonons or of electrons. In the first case, the integration over the phonon degrees of freedom is performed exactly and in the large mass limit of the heavy particle it gives rise to an ohmic effective action which includes a nonlocal self-interacting term whose strength is the classical friction coefficient. In the second case, the integration over the electronic degrees of freedom is more difficult; we are able to derive an approximate effective action for the heavy particle in two different limiting cases: i) arbitrary large coupling between heavy particle and electrons and linear dissipation; ii) weak coupling and nonlinear dissipation. In i) we obtain an effective action for the particle equal to that found for the phonons but with a friction coefficient given by that of a classical heavy particle in a fermionic bath. In ii) we obtain a nonlinear, but still ohmic, dissipative term. Using an instanton approach we evaluate the mobility (and the diffusion coefficient) of the particle, whose temperature dependence shows a crossover from diffusive to localized behaviour at a critical value of the friction. Finally we discuss whether the electronic and phononic frictions can reach such a critical value. To speed up publication, the authors have agreed not to receive proofs which have been supervised by the Scientific Committee.     

Nonlinear Lattice Effect on Ground State of One-Dimensional Electron-Phonon System

We study the nonlinear lattice effect on the ground state in a one-dimensional spinless Holstein model with nonadiabitical coupling and squeezing by means of the parameter variational approach. Our results show that the introduction of a hard quartic term in the lattice potential increases the ground state energy of the system when electron-phonon coupling is strong, and the increment is sensitive to the magnitude of the lattice quartic force constant. In this case the nonlinear lattice effects should be taken into account to describe satisfactorily some physical properties of the coupling system.     

Z(N) topological excitations in Yang-Mills theories: duality and confinement

We investigate the properties of Z(N) topological excitations in Wilson's lattice formulation of SU(N) Yang-Mills theories. We exhibit the Z(N) topological excitations as exact classical solutions on the lattice. After giving detailed qualitative discussions about the Z(N) excitations and their relevance to confinement, we investigate the Z(N) lattice gauge theories with the Wilson action and show that Z(2), Z(3) and Z(4) models are self-dual systems. (The self-duality of the Z(2) case has been known previously.) This property enables us to locate the critical points exactly in those systems under the assumption that the phase transition occurs at only one point in the coupling constant space. We then derive the effective action for the Z(N) topological excitations in the lattice SU(N) Yang-Mills theories in the steepest descent approximation. The critical coupling constants in the SU(N) models corresponding to the phase transition caused by the Z(N) excitations are estimated by using the information on the Z(N) models with the Wilson action. It is quite probable that the estimated value $\text{g}{}_{\mathrm{<mtext>r</mtext>}}{}^2\text{/4π}{}^2\text{～}\text{1}\text{31}$ (for SU(3)) is an upper bound. This indicates that the Wilson model of the SU(3) gauge field can be effective action of the QCD gluons which exhibit permanent quark confinement and, at the same time, freedom up to the distance characterized by the energy, at least, ～1 TeV.     

Investigation of the $B_{c}\rightarrow\chi_{c2} l \overline {\nu} $ transition via QCD sum rules

We study the spectrum of the minimal supersymmetric extension of the Carroll–Field–Jackiw model for Electrodynamics with a topological Chern–Simons-like Lorentz-symmetry violating term. We identify a number of independent background fermion condensates, work out the gaugino dispersion relation and propose a photonic effective action to consider aspects of confinement induced by the SUSY background fermion condensates, which also appear to signal Lorentz-symmetry violation in the photino sector of the action. Our calculations of the static potential are carried out within the framework of the gauge-invariant but path-dependent variables formalism which are alternative to the Wilson loop approach. Our results show that the interaction energy contains a linear term leading to the confinement of static probe charges.     

Lattice Yang-Mills theory at nonzero temperature and the confinement problem

We discuss finite temperature lattice Yang-Mills theory with special attention to the confinement problem. The relationship between the confinement criteria of Wilson, Polyakov, and 't Hooft is clarified by establishing a string of inequalities between the corresponding string tensions. The close connection between finite temperature Yang-Mills models and spin models is exploited to obtain new and rather sharp upper bounds for the critical coupling constant above which there is confinement. This same analogy also allows us to establish infrared bounds for the gauge models that yield a lower bound for this critical coupling and thereby show the existence of a weak coupling regime without confinement at nonzero temperature in three or more space dimensions. Finally we discuss extension of our results to other forms of the lattice action, the Hamiltonian lattice models of Kogut and Susskind and 't Hooft'sN → ∞ limit.