Chiral symmetry breaking and topology for all N

We investigate spontaneous chiral symmetry breaking in SU(N) gauge theories at large N using overlap fermions. The exact zero modes and the low-lying modes of the Dirac operator provide the tools to gain insight into the interplay between chiral symmetry breaking and topology. We find that topology indeed drives chiral symmetry breaking at N=3 as well as at large N. By comparing the results on various volumes and at different lattice spacings we are able to show that our conclusions are not affected by finite volume effects and also hold in the continuum limit. We then address the question whether the topology can be usefully described in terms of instantons.Comment: Talk at Lattice 2003 (chiral); 3 pages, 2 figures, espcrc2.st

Glueballs and k-strings in SU(N) gauge theories : calculations with improved operators

We test a variety of blocking and smearing algorithms for constructing glueball and string wave-functionals, and find some with much improved overlaps onto the lightest states. We use these algorithms to obtain improved results on the tensions of k-strings in SU(4), SU(6), and SU(8) gauge theories. We emphasise the major systematic errors that still need to be controlled in calculations of heavier k-strings, and perform calculations in SU(4) on an anisotropic lattice in a bid to minimise one of these. All these results point to the k-string tensions lying part-way between the `MQCD' and `Casimir Scaling' conjectures, with the power in 1/N of the leading correction lying in [1,2]. We also obtain some evidence for the presence of quasi-stable strings in calculations that do not use sources, and observe some near-degeneracies between (excited) strings in different representations. We also calculate the lightest glueball masses for N=2, ...,8, and extrapolate to N=infinity, obtaining results compatible with earlier work. We show that the N=infinity factorisation of the Euclidean correlators that are used in such mass calculations does not make the masses any less calculable at large N.Comment: 49 pages, 15 figure

Confining strings in SU(N) gauge theories

We calculate the string tensions of $k$-strings in SU($N$) gauge theories in both 3 and 4 dimensions. In D=3+1, we find that the ratio of the $k=2$ string tension to the $k = 1$ fundamental string tension is consistent, at the $2 \sigma$ level, with both the M(-theory)QCD-inspired conjecture and with `Casimir scaling'. In D=2+1 we see a definite deviation from the MQCD formula, as well as a much smaller but still significant deviation from Casimir scaling. We find that in both D=2+1 and D=3+1 the high temperature spatial $k$-string tensions also satisfy approximate Casimir scaling. We point out that approximate Casimir scaling arises naturally if the cross-section of the flux tube is nearly independent of the flux carried, and that this will occur in an effective dual superconducting description, if we are in the deep-London limit. We estimate, numerically, the intrinsic width of $k$-strings in D=2+1 and indeed find little variation with $k$. In addition to the stable $k$-strings we investigate some ofthe unstable strings, finding in D=2+1 that they satisfy (approximate) Casimir scaling. We also investigate the basic assumption that confining flux tubes are described by an effective string theory at large distances. We estimate the coefficient of the universal L\"uscher correction from periodic strings that are longer than 1 fermi, and find $c_L=0.98(4)$ in D=3+1 and $c_L=0.558(19)$ in D=2+1. These values are within $2 \sigma$ of the simple bosonic string values and are inconsistent with other simple effective string theories.Comment: 57 pages, 11 figures. Errors on fits reduced by altering the analysis to a standard one. Conclusions unchanged; note addedchanged. Some typos correcte

Calibration of Smearing and Cooling Algorithms in SU(3)-Color Gauge Theory

The action and topological charge are used to determine the relative rates of standard cooling and smearing algorithms in pure SU(3)-color gauge theory. We consider representative gauge field configurations on $16^3\times 32$ lattices at $\beta=5.70$ and $24^3\times 36$ lattices at $\beta=6.00$. We find the relative rate of variation in the action and topological charge under various algorithms may be succinctly described in terms of simple formulae. The results are in accord with recent suggestions from fat-link perturbation theory.Comment: RevTeX, 25 pages, 22 figures, full resolution jpeg version of Fig. 22 can be obtained from http://www.physics.adelaide.edu.au/cssm/papers_etc/SmearingComp.jp

Topological Structure of the SU(3) Vacuum

We investigate the topological structure of the vacuum in SU(3) lattice gauge theory. We use under-relaxed cooling to remove the high-frequency fluctuations and a variety of "filters" to identify the topological charges in the resulting smoothened field configurations. We find a densely packed vacuum with an average instanton size, in the continuum limit, of about 0.5 fm. The density at large sizes decreases as a large inverse power of the size. At small sizes we see some sign of a trend towards the asymptotic perturbative behaviour. We find that an interesting polarisation phenomenon occurs: the large topological charges tend to have, on the average, the same sign and are over-screened by the smaller charges which tend to have, again on the average, the opposite sign to the larger instantons. We also calculate the topological susceptibility for which we obtain a continuum value of about 187 MeV. We perform the calculations for various volumes, lattice spacings and numbers of cooling sweeps, so as to obtain some control over the associated systematic errors. The coupling range is from beta=6.0 to beta=6.4 and the lattice volumes range from 16x16x16x48 to 32x32x32x64.Comment: LaTeX. Self-unpacking, uuencoded tar-compressed fil

Large N reduction in the continuum three dimensional Yang-Mills theory

Numerical and theoretical evidence leads us to propose the following: Three dimensional Euclidean Yang-Mills theory in the planar limit undergoes a phase transition on a torus of side $l=l_c$. For $l>l_c$ the planar limit is $l$-independent, as expected of a non-interacting string theory. We expect the situation in four dimensions to be similar.Comment: 4 pages, latex file, two figures, version to appear in Phys. Rev. Let

The 2-dimensional non-linear sigma-model on a random latice

The O(n) non-linear $\sigma$-model is simulated on 2-dimensional regular and random lattices. We use two different levels of randomness in the construction of the random lattices and give a detailed explanation of the geometry of such lattices. In the simulations, we calculate the mass gap for $n=3, 4$ and 8, analysing the asymptotic scaling of the data and computing the ratio of Lambda parameters $\Lambda_{\rm random}/\Lambda_{\rm regular}$. These ratios are in agreement with previous semi-analytical calculations. We also numerically calculate the topological susceptibility by using the cooling method.Comment: REVTeX file, 23 pages. 13 postscript figures in a separate compressed tar fil

Revisiting glueball wave functions at zero and finite temperature

We study the sizes and thermal properties of glueballs in a three dimensional compact Abelian gauge model on improved lattice. We predict the radii of $\sim 0.60$ and $\sim 1.12$ in the units of string tension, or $\sim 0.28$ and $\sim 0.52$ fm, for the scalar and tensor glueballs, respectively. We perform a well controlled extrapolation of the radii to the continuum limit and observe that our results agree with the predicted values. Using Monte Carlo simulations, we extract the pole-mass of the lowest scalar and tensor glueballs from the temporal correlators at finite temperature. We see a clear evidence of the deconfined phase, and the transition appears to be similar to that of the two-dimensional XY model as expected from universality arguments. Our results show no significant changes in the glueball wave functions and masses in the deconfined phase.Comment: 8 pages, 10 figure

Domain walls and perturbation theory in high temperature gauge theory: SU(2) in 2+1 dimensions

We study the detailed properties of Z_2 domain walls in the deconfined high temperature phase of the d=2+1 SU(2) gauge theory. These walls are studied both by computer simulations of the lattice theory and by one-loop perturbative calculations. The latter are carried out both in the continuum and on the lattice. We find that leading order perturbation theory reproduces the detailed properties of these domain walls remarkably accurately even at temperatures where the effective dimensionless expansion parameter, g^2/T, is close to unity. The quantities studied include the surface tension, the action density profiles, roughening and the electric screening mass. It is only for the last quantity that we find an exception to the precocious success of perturbation theory. All this shows that, despite the presence of infrared divergences at higher orders, high-T perturbation theory can be an accurate calculational tool.Comment: 75 pages, LaTeX, 14 figure

Infrared behavior of the gluon propagator in lattice Landau gauge: the three-dimensional case

We evaluate numerically the three-momentum-space gluon propagator in the lattice Landau gauge, for three-dimensional pure-SU(2) lattice gauge theory with periodic boundary conditions. Simulations are done for nine different values of the coupling $\beta$, from $\beta = 0$ (strong coupling) to $\beta = 6.0$ (in the scaling region), and for lattice sizes up to $V = 64^3$. In the limit of large lattice volume we observe, in all cases, a gluon propagator decreasing for momenta smaller than a constant value $p_{dec}$. From our data we estimate $p_{dec} \approx 350$ MeV. The result of a gluon propagator decreasing in the infrared limit has a straightforward interpretation as resulting from the proximity of the so-called first Gribov horizon in the infrared directions.Comment: 14 pages, BI-TP 99/03 preprint, correction in the Acknowledgments section. To appear in Phys.Rev.