Particle theory

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.