No abstract

We calculate the next-to-next-to-leading correction to the expectation value of the Polyakov loop or equivalently to the free energy of a static charge. This correction is of order g 5 . We show that up to this order the free energy of the static charge is proportional to the quadratic Casimir operator of the corresponding representation. We also compare our perturbative result with the most recent lattice results in SU(3) gauge theory.

We study the Polyakov loop correlator in the weak coupling expansion and show how the perturbative series reexponentiates into singlet and adjoint contributions. We calculate the order g 7 correction to the Polyakov loop correlator in the short distance limit. We show how the singlet and adjoint free energies arising from the reexponentiation formula of the Polyakov loop correlator are related to the gauge invariant singlet and octet free energies that can be defined in pNRQCD, namely we find that the two definitions agree at leading order in the multipole expansion, but differ at first order in the quark-antiquark distance.

In finite-temperature field theory, the cyclic Wilson loop is defined as a rectangular Wilson loop spanning the whole compactified time direction. In a generic non-abelian gauge theory, we calculate the perturbative expansion of the cyclic Wilson loop up to order g^4. At this order and after charge renormalization, the cyclic Wilson loop is known to be ultraviolet divergent. We show that the divergence is not associated with cusps in the contour but is instead due to the contour intersecting itself because of the periodic boundary conditions. One consequence of this is that the cyclic Wilson loop mixes under renormalization with the correlator of two Polyakov loops. The resulting renormalization equation is tested up to order g^6 and used to resum the leading logarithms associated with the intersection divergence. Implications for lattice studies of this operator, which may be relevant for the phenomenology of quarkonium at finite temperature, are discussed.Comment: 30 pages, 21 figures. Reference and note added, journal versio