A. Morel

Flavours of lagrangian Susskind fermions

Abstract It is shown in this paper how to write the Susskind fermionic action explicitly in terms of flavour Dirac fields defined on hypercubes in position space. The remnant continuous global symmetry is identified with a U(1) V ⊗U(1) A group, where the axial symmetry is flavour non-singlet. This construction allows us to identify the equantum numbers of states found in dynamical calculations for SU( N ) gauge theories, and the currents associated with the above global symmetry. It is also used, in the strong-coupling limit, to compute the decay constant of the pseudo-scalar Goldstone boson associated with the spontaneous breakdown of the U(1) A symmetry. We stress that our construction of flavours leads to a quark propagator which is continuous on the edges of the Brillouin zone, unlike the one obtained by assigning different flavours to different parts of this zone.

SPONTANEOUS CHIRAL SYMMETRY-BREAKING FOR A U(N) GAUGE-THEORY ON A LATTICE

Abstract We study the breakdown of chiral invariance by calculating, in the infinite coupling, large-N limit, the generating functional of a U(N) gauge theory with one fermion, expressed on a lattice with the naive, chiral symmetric action. We compute the link integral over the gauge fields and the expression obtained after the integration over the fermions is recast under the form of a generating functional for bosonic fields. Then, a saddle-point method allows the calculation of the order parameter 〈 ψ ψ〉 for which a non-zero value signals the spontaneous breakdown of chiral symmetry. The analysis of the fluctuations around the saddle point allows one to exhibit the Goldstone modes corresponding to those global symmetries of the fermionic lattice action which are simultaneously broken.

A numerical simulation of quenched SU(2) lattice gauge theory

Abstract We present the results of a large-statistics numerical simulation for a quenched SU(2) gauge theory with staggered quarks. The use of two lattices of size 8 3 × 16 and 12 3 × 24 allows us to show the absence of any measurable finite size effect at β = 2.3. A study of the β-dependence ( β = 2.1–2.4) on the smallest lattice leads to a scaling behaviour for 〈 χ χ〉 and the ϱ-mass for β ⪆ 2.2 , but not for the π-decay constant ƒ π . We perform a detailed analysis of mesonic correlation functions in terms of the quantum numbers of the corresponding continuum theory. It allows us to interpret our numerical results for non-local mesonic operators, leading to strong evidence for various very light flavoured pseudo-scalars on the lattice, in accordance with a Nambu-Goldstone realization of full chiral symmetry in the continuum. Special care is taken in error estimates, and possible systematic errors are discussed.

THE STRONG COUPLING EXPANSION OF LATTICE GAUGE-THEORIES WITH SUSSKIND FERMIONS

We consider Susskind fermions interacting with an SU(N) gauge field on a d-dimensional lattice. We compute 〈χχ〉 and the meson propagator up to second order in the inverse coupling g2, using a 1/d expansion technique. The baryon mass is given at first order in 1/d and 1/g2. The corrections to leading order results are found to be quite appreciable. For SU(3) at g2⋍1, 〈χχ〉 and the meson spectrum are quite close to the values found by MC calculations. We find a baryon mass at 1040 MeV once the ϱ mass has been fixed.

THE STRONG-COUPLING LIMIT OF GAUGE-THEORIES WITH FERMIONS ON A LATTICE

Abstract Low-energy properties of the lattice gauge theories U(N) or SU(N) with fermions are derived in the infinite-coupling limit from a 1 d expansion of Greens functions. Spontaneous global symmetry breaking is shown to occur. The analytically computed meson spectrum nearly coincides with the one obtained by Monte Carlo methods at finite coupling. Estimates of the baryon mass and pion decay constant are also given.

Continuum symmetries of lattice models with staggered fermions

Abstract The validity of the flavour interpretation of staggered fermions is discussed in terms of the discrete symmetries of the interaction terms. Some aspects of the embedding of these symmetries in the symmetry group of the continuum limit are clarified. An explicit calculation, at first non-trivial order in 1/ N , of the four-point function for a latticized Gross-Neveu model yields the same result in the continuum limit as the continuum theory for 2 N fermions. A proof is then given that flavour and C , P , and T symmetries are restored in the continuum limit of 2-point correlation functions, for interactions, including the case of 4-dimensional QCD, which respect the discrete symmetries of the free action.

High temperature 3D QCD: dimensional reduction at work

We investigate the three-dimensional SU(3) gauge theory at finite temperature in the framework of dimensional reduction. The large scale propel ties of this theory are expected to be conceptually more complicated than in four dimensions. The dimensionally reduced action is computed in closed analytical form. The resulting effective two-dimensional theory is studied numerically both in the electric and magnetic sector. We find that dimensional reduction works excellently down to temperatures of 1.5 times the deconfinement phase transition temperature and even on rather short length scales. We obtain strong evidence that for QCD(3), even at high temperature the colour averaged potential is represented by the exchange of a single state, at variance with the usual Debye screening picture involving a pair of electric gluons

How do clusters look in semi-inclusive cross sections?

Abstract It is shown how semi-inclusive quantities can be used in order to learn something about the decay of clusters in independent cluster emission models. The average multiplicity, and binomial moments, of the cluster decay distribution are proved to increase with the total multiplicity. The rate of increase can be looked at through semi-inclusive correlation measurements, and is shown to contain interesting information about the clusters.

Light psuedoscalars and symmetry restoration in SU(2) lattice QCD

Abstract We present evidence for the existence of light, non-Goldstone, pseudo-scalars, and for flavour symmetry restoration as β is increased from 2.1 to 2.3, for the SU(2) lattice gauge theory with (quenched) Susskind fermions, by means of a numerical simulation.

Thermodynamics of SU(3) gauge theory in 2+1 dimensions

The pressure, and the energy and entropy densities are determined for the SU(3)SU(3) gauge theory in 2+12+1 dimensions from lattice Monte Carlo calculations in the interval 0.6⩽T/Tc⩽150.6⩽T/Tc⩽15. The finite temperature lattices simulated have temporal extent Nτ=2Nτ=2, 4, 6 and 8, and spatial volumes NS2 such that the aspect ratio is NS/Nτ=8NS/Nτ=8. To obtain the thermodynamical quantities, we calculate the averages of the temporal plaquettes PτPτ and the spatial plaquettes PSPS on these lattices. We also need the zero temperature averages of the plaquettes P0P0, calculated on symmetric lattices with Nτ=NSNτ=NS. We discuss in detail the finite size (NSNS-dependent) effects. These disappear exponentially. For the zero temperature lattices we find that the coefficient of NSNS in the exponent is of the order of the glueball mass. On the finite temperature lattices it lies between the two lowest screening masses. For the aspect ratio equal to eight, the systematic errors coming from the finite size effects are much smaller than our statistical errors. We argue that in the continuum limit, at high enough temperature, the pressure can be parametrized by the very simple formula p=T3(a−bTc/T)p=T3(a−bTc/T) where a and b are two constants. Using the thermodynamical identities for a large homogeneous system, this parametrization then determines the other thermodynamical variables in the same temperature range.