Dr Michael Teper

Abstract:

We show that, under certain general assumptions, any sensible lattice Dirac operator satisfies a generalized form of the Ginsparg-Wilson relation (GWR). Those assumptions, on the other hand, are mostly dictated by large momentum behaviour considerations. We also show that all the desirable properties often deduced from the standard GWR hold true of the general case as well; hence one has, in fact, more freedom to modify the form of the lattice Dirac operator, without spoiling its nice properties. Our construction, a generalized Ginsparg-Wilson relation (GGWR), is satisfied by some known proposals for the lattice Dirac operator. We discuss some of these examples, and also present a derivation of the GGWR in terms of a renormalization group transformation with a blocking which is not diagonal in momentum space, but nevertheless commutes with the Dirac operator.

Abstract:

We calculate the k = 2 string tension in SU(4) and SU(5) gauge theories in 3 + 1 dimensions, and compare it to the k = 1 fundamental string tension. We find, from the continuum extrapolation of our lattice calculations, that σk=2/σf = 1.40±0.08 in the SU(4) gauge theory, and that σk=2/σf = 1.56 ± 0.10 in SU(5). We remark upon the way this might constrain the dynamics of confinement and the intriguing implications it might have for the mass spectrum of SU(N) gauge theories. We also note that these results agree closely with the MQCD-inspired conjecture that the SU(N) string tension varies as σk α sin(πk/N). © 2001 Published by Elsevier Science B.V.

Abstract:

We calculate the euclidean action of a pair of ℤ2 monopoles (instantons), as a function of their spatial separation, in D = 2 + 1 SU(2) lattice gauge theory. We do so both above and below the deconfining transition at T = Tc. At high T, and at large separation, we find that the monopole "interaction" grows linearly with distance: the flux between the monopoles forms a flux tube (exactly like a finite portion of a ℤ2 domain wall) so that the monopoles are linearly confined. At short distances the interaction is well described by a Coulomb interaction with, at most, a very small screening mass, possibly equal to the Debye electric screening mass. At low T the interaction can be described by a simple screened Coulomb (i.e. Yukawa) interaction with a screening mass that can be interpreted as the mass of a "constituent gluon". None of this is unexpected, but it helps to resolve some apparent controversies in the recent literature.