Strong-coupling Lattice Gauge Theory Research Articles

Linear confinement in the partially-deconfined phase

We consider the partially-deconfined saddle of large-N pure Yang-Mills theory lying between confined and deconfined phases, in which the color degrees of freedom split into confined and deconfined sectors. Based on the microscopic mechanism of deconfinement, we argue that a flux tube is formed in the confined sector and a linear confinement potential is generated. The string tension should not depend on the size of the confined sector. We provide evidence for the case of the finite-temperature strong-coupling lattice gauge theory. In particular, we make analytic predictions assuming linear confinement in the confined sector, and then confirm these by numerical simulations. We discuss some implications of the conjecture to QCD and holography.

K-string tensions and the1/Nexpansion

We address the question of whether the large-N expansion in pure SU(N) gauge theories requires that k-string tensions must have a power series expansion in 1/N^2, as in the sine law, or whether 1/N contributions are also allowable, as in Casimir scaling. We find that k-string tensions may, in fact, have 1/N corrections, and consistency with the large-N expansion in the open-string sector depends crucially on an exact cancellation, which we will prove, among terms involving odd powers of 1/N in particular combinations of Wilson loops. It is shown how these cancellations are fulfilled, and consistency with the large-N expansion achieved, in a concrete example, namely, strong-coupling lattice gauge theory with the heat-kernel action. This is a model which has both a 1/N^2 expansion and Casimir scaling of the k-string tensions. Analysis of the closed string channel in this model confirms our conclusions, and provides further insights into the large-N dependence of energy eigenstates and eigenvalues.

What are the confining field configurations of strong-coupling lattice gauge theory?

Starting from the strong-coupling SU(2) Wilson action in D=3 dimensions, we derive an effective, semi-local action on a lattice of spacing L times the spacing of the original lattice. It is shown that beyond the adjoint color-screening distance, i.e. for $L \ge 5$, thin center vortices are stable saddlepoints of the corresponding effective action. Since the entropy of these stable objects exceeds their energy, center vortices percolate throughout the lattice, and confine color charge in half-integer representations of the SU(2) gauge group. This result contradicts the folklore that confinement in strong-coupling lattice gauge theory, for D>2 dimensions, is simply due to plaquette disorder, as is the case in D=2 dimensions. It also demonstrates explicitly how the emergence and stability of center vortices is related to the existence of color screening by gluon fields.

Bounding the constituent quark mass

The constituent quark mass M can be defined by the large distance behavior of the quark propagator, in some chosen gauge. I prove that the constituent mass, so defined, is bounded from below by one half of the mass of the pseudoscalar bound state: m π ⩽2 M q. The bound itself is independent of the choice of gauge. An example from strong-coupling lattice gauge theory is discussed, as well as the extension of the inequality to finite temperature.

From asymptotic freedom to quark confinement

Asymptotic freedom is the perturbative expression of paramagnetic screening by the QCD vacuum. When extended to large external fields the perturbative analysis leads to a catastrophe owing to the appearance of negative eigenvalues of the matrix describing the fluctuations of the gluonic field. This is met by a self-consistently determined magnetic-moment density. There results almost complete screening of the external field and the action is dominated by fluctuations of the magnetic moment. Such behaviour is more typical of very strong coupling e ⪢ 1 rather than that expected for e = O(1), the latter being the effective coupling at the QCD length scale. This kind of situation arises in the response to large Wilson loops, so that the derivation of the area law from strong-coupling lattice gauge theory can be rationalized.

Hadronic matrix elements at strong coupling

It is proposed to evaluate hadronic matrix elements using strong coupling lattice gauge theory. The calculation of f π is described in detail to illustrate our method, and it is then used to calculate the π +-π 0 mass difference. The relevance of the result to Monte Carlo calculations and the experimental data is discussed.

Surface description of gauge theories

The partition function of non-abelian gauge theory is expressed, in the continuum limit, as a sum over surfaces which are swept out by the propagation of electric flux rings. Each flux surface is described by a two-dimensional continuum gauge theory, confined to that particular surface. The gauge field can then be integrated out; however, for closed and intersecting surfaces interesting complications arise, which reveal an algebraic structure typical of strong-coupling lattice gauge theory.

Composite models of quarks and leptons and strong-coupling lattice gauge theories

We extend a previous variational block-spin analysis of the realization of chiral symmetry in a strong-coupling lattice gauge theory to models which have been suggested as possibly describing massless composite fermions. In all cases we find massive fermion composites and spontaneous breaking of chiral symmetry. We also discuss the relevance of this result to the continuum limit.

Chiral symmetry breaking in the action formulation of lattice gauge theory

We show, in the euclidean path-integral formulation of strong-coupling lattice gauge theory, that continuous chiral symmetry is dynamically broken, and obtain the standard current algebra result that m pseudo-Goldstone 2 ∼ m quark 〈 ψψ〉 . We also remark that the center of the gauge group does not seem very relevant for this result; chiral symmetry breaking is a property of strong-coupling lattice theories both in the case where quark color is confined, and also in the case where it is screened by gauge field fluctuations.

Approximate dynamical symmetry in lattice quantum chromodynamics

We discuss the phenomenological implications of an approximate SU(6)\ifmmode\times\else\texttimes\fi{}SU(6)\ifmmode\times\else\texttimes\fi{}U(1) symmetry of hadron physics which remains after dynamical symmetry breaking in the strong-coupling lattice gauge theory. This symmetry is similar to but differs in an essential fashion from previous versions of SU(6) \ifmmode\times\else\texttimes\fi{} SU(6) \ifmmode\times\else\texttimes\fi{} or $\mathrm{SU}{(6)}_{W}$. The difference resolves some of the problems of the older schemes---for example, although we obtain the "good" result $\frac{{\ensuremath{\mu}}_{p}}{{\ensuremath{\mu}}_{n}}=\ensuremath{-}\frac{3}{2}$, we avoid the "bad" result $\frac{{g}_{A}}{{g}_{V}}=\ensuremath{-}\frac{5}{3}$. We find that mesons are better approximated as irreducible representations of an $\mathrm{SU}{(6)}_{W}$ than static SU(6). Vector mesons are pseudo-Goldstone bosons in our scheme, which explains why the sum rules for their masses should be written in terms of mass squared, like those of the pseudoscalars.

Dynamical breaking of chiral symmetry in lattice gauge theories

We generalize the variational block-spin methods developed earlier to show that spontaneous breaking of chiral symmetries and the associated massless Goldstone particles arise naturally within the context of strong-coupling lattice gauge theory. Our calculations show the importance of preserving continuous chiral symmetry when transcribing the quantum chromodynamics (QCD) of massless quarks onto the lattice. The meson sector is analyzed for both one and three spatial dimensions, and the criteria for recognizing Nambu-Goldstone phenomena are identified. The relation of these results to continuum QCD and to general properties of observed hadrons is also discussed.

Large-scale vacuum structure and new calculational techniques in lattice SU( N) gauge theory

By exponentiating infinite series of vacuum diagrams in strong-coupling lattice gauge theory, an expression for the ground state is obtained containing new information about long-wavelength, large-scale vacuum fluctuations. It is found that lattice vacuum fluctuations are dominated by monopole configurations, on scales large compared to the lattice spacing. An efficient alternative to the standard Kogut-Susskind perturbative expansion is developed, which avoids the use of group integrations. A possible non-perturbative extension of this technique, applicable to intermediate couplings, is discussed.