8 research outputs found
Polyakov soldering and second order frames : the role of the Cartan connection
The so-called "soldering" procedure performed by A.M. Polyakov in [1] for a
SL(2,R)-gauge theory is geometrically explained in terms of a Cartan connection
on second order frames of the projective space RP^1. The relationship between a
Cartan connection and the usual (Ehresmann) connection on a principal bundle
allows to gain an appropriate insight into the derivation of the genuine "
diffeomorphisms out of gauge transformations" given by Polyakov himself.Comment: Accept\'e pour publication dans Lett. Math. Phy
Bound state equation in the Wilson loop approach with minimal surfaces
The large-distance dynamics in quarkonium systems is investigated, in the
large N limit, through the saturation of Wilson loop averages by minimal
surfaces. Using a representation for the quark propagator in the presence of
the external gluon field based on the use of path-ordered phase factors, a
covariant three-dimensional bound state equation of the Breit-Salpeter type is
derived, in which the interaction potentials are provided by the
energy-momentum vector of the straight segment joining the quark to the
antiquark and carrying a constant linear energy density, equal to the string
tension. The interaction potentials are confining and reduce to the linear
vector potential in the static case and receive, for moving quarks,
contributions from the moments of inertia of the straight segment. The
self-energy parts of the quark propagators induce spontaneous breakdown of
chiral symmetry with a mechanism identical to that of the exchange of one
Coulomb-gluon. The nonrelativistic and ultrarelativistic properties of the
bound state spectrum are studied.Comment: 57 pages, 7 figure