arXiv subjects

Michael Teper

Publications and source records attributed to Michael Teper.

61 records · Page 4Linked to original sources

arXiv2005

Casimir scaling of domain wall tensions in the deconfined phase of D=3+1 SU(N) gauge theories

We perform lattice calculations of the spatial 't Hooft k-string tensions in the deconfined phase of SU(N) gauge theories for N=2,3,4,6. These equal (up to a factor of T) the surface tensions of the domain walls between the corresponding (Euclidean) deconfined phases. For T much larger than Tc our results match on to the known perturbative result, which exhibits Casimir Scaling, being proportional to k(N-k). At lower T the coupling becomes stronger and, not surprisingly, our calculations show large deviations from the perturbative T-dependence. Despite this we find that the behaviour proportional to k(N-k) persists very accurately down to temperatures very close to Tc. Thus the Casimir Scaling of the 't Hooft tension appears to be a `universal' feature that is more general than its appearance in the low order high-T perturbative calculation. We observe the `wetting' of these k-walls at T around Tc and the (almost inevitable) `perfect wetting' of the k=N/2 domain wall. Our calculations show that as T tends to Tc the magnitude of the spatial `t Hooft string tension decreases rapidly. This suggests the existence of a (would-be) 't Hooft string condensation transition at some temperature which is close to but below Tc. We speculate on the `dual' relationship between this and the (would-be) confining string condensation at the Hagedorn temperature that is close to but above Tc.

hep-lat↗

arXiv2004

Confinement and the effective string theory in SU(N->oo) : a lattice study

We calculate in the SU(6) gauge theory the mass of the lightest flux loop that winds around a spatial torus, as a function of the torus size, taking care to achieve control of the main systematic errors. For comparison we perform a similar calculation in SU(4). We demonstrate approximate linear confinement and show that the leading correction is consistent with what one expects if the flux tube behaves like a simple bosonic string at long distances. We obtain similar but less accurate results for stable (k-)strings in higher representations. We find some evidence that for k>1 the length scale at which the bosonic string correction becomes dominant increases as N increases. We perform all these calculations not just for long strings, up to about 2.5`fm' in length, but also for shorter strings, down to the minimum length, lc = 1/Tc, where Tc is the deconfining temperature. We find that the mass of the ground-state string, at all length scales, is not very far from the simple Nambu-Goto string theory prediction, and that the fit improves as N increases from N=4 to N=6. We estimate the mass of the first excited string and find that it also follows the Nambu-Goto prediction, albeit more qualitatively. We comment upon the significance of these results for the string description of SU(N) gauge theories in the limit of infinite N.

hep-lat↗

arXiv2004

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.

hep-lat↗

arXiv2004

Topology of SU(N) gauge theories at T=0 and T=Tc

We calculate the topological charge density of SU(N) lattice gauge fields for values of N up to N=8. Our T=0 topological susceptibility appears to approach a finite non-zero limit at N=infinity that is consistent with earlier extrapolations from smaller values of N. Near the deconfining temperature Tc we are able to investigate separately the confined and deconfined phases, since the transition is quite strongly first order. We find that the topological susceptibility of the confined phase is always very similar to that at T=0. By contrast, in the deconfined phase at larger N there are no topological fluctuations except for rare, isolated and small instantons. This shows that as N->infinity the large-T suppression of large instantons and the large-N suppression of small instantons overlap, even at T=Tc, so as to suppress all topological fluctuations in the deconfined phase. In the confined phase by contrast, the size distribution is much the same at all T, becoming more peaked as N grows, suggesting that D(rho) is proportional to a delta function at N=infinity, centered on rho close to 1/Tc.

hep-lat↗

arXiv2003

The high temperature phase transition in SU(N) gauge theories

We calculate the continuum value of the deconfining temperature in units of the string tension for SU(4), SU(6) and SU(8) gauge theories, and we recalculate its value for SU(2) and SU(3). We find that the $N$-dependence for $2 \leq N \leq 8$ is well fitted by $T_c/\sqrt{sigma} = 0.596(4) + 0.453(30)/N^2$, showing a rapid convergence to the large-N limit. We confirm our earlier result that the phase transition is first order for $N \geq 3$ and that it becomes stronger with increasing $N$. We also confirm that as $N$ increases the finite volume corrections become rapidly smaller and the phase transition becomes visible on ever smaller volumes. We interpret the latter as being due to the fact that the tension of the domain wall that separates the confining and deconfining phases increases rapidly with $N$. We speculate on the connection to Eguchi-Kawai reduction and to the idea of a Master Field.

hep-lat↗

arXiv2002

Topology and chiral symmetry breaking in SU(N) gauge theories

We study the low-lying eigenmodes of the lattice overlap Dirac operator for SU(N) gauge theories with N=2,3,4 and 5 colours. We define a fermionic topological charge from the zero-modes of this operator and show that, as N grows, any disagreement with the topological charge obtained by cooling the fields, becomes rapidly less likely. By examining the fields where there is a disagreement, we are able to show that the Dirac operator does not resolve instantons below a critical size of about rho = 2.5 a, but resolves the larger, more physical instantons. We investigate the local chirality of the near-zero modes and how it changes as we go to larger N. We observe that the local chirality of these modes, which is prominent for SU(2) and SU(3), becomes rapidly weaker for larger N and is consistent with disappearing entirely in the limit of N -> infinity. We find that this is not due to the observed disappearance of small instantons at larger N.

hep-lat↗

arXiv1998

Glueball masses and other physical properties of SU(N) gauge theories in D=3+1: a review of lattice results for theorists

We summarise what lattice simulations have to say about the physical properties of continuum SU(N) gauge theories in 3+1 dimensions. The quantities covered are: the glueball mass spectrum, the confining string tension, the temperature at which the theory becomes deconfined, the topological susceptibility, the value of the scale Lambda{MS-bar} that governs the rate at which the coupling runs and the r0 parameter that characterises the static quark potential at intermediate distances.

hep-th↗