String Effects in the Wilson Loop: a high precision numerical test

We test numerically the effective string description of the infrared limit of lattice gauge theories in the confining regime. We consider the 3d Z(2) lattice gauge theory, and we define ratios of Wilson loops such that the predictions of the effective string theory do not contain any adjustable parameters. In this way we are able to obtain a degree of accuracy high enough to show unambiguously that the flux--tube fluctuations are described, in the infrared limit, by an effective bosonic string theory.Comment: 19 pages, LaTeX file + two .eps figure

Generalized quark-antiquark potential at weak and strong coupling

We study a two-parameter family of Wilson loop operators in N=4 supersymmetric Yang-Mills theory which interpolates smoothly between the 1/2 BPS line or circle and a pair of antiparallel lines. These observables capture a natural generalization of the quark-antiquark potential. We calculate these loops on the gauge theory side to second order in perturbation theory and in a semiclassical expansion in string theory to one-loop order. The resulting determinants are given in integral form and can be evaluated numerically for general values of the parameters or analytically in a systematic expansion around the 1/2 BPS configuration. We comment about the feasibility of deriving all-loop results for these Wilson loops.Comment: 43 pages: 15 comprising the main text and 25 for detailed appendice

The one loop MSbar static potential in the Gribov-Zwanziger Lagrangian

We compute the static potential in the Gribov-Zwanziger Lagrangian as a function of the Gribov mass, gamma, in the MSbar scheme in the Landau gauge at one loop. The usual gauge independent one loop perturbative static potential is recovered in the limit as gamma -> 0. By contrast the Gribov-Zwanziger static potential contains the term gamma^2/(p^2)^2. However, the linearly rising potential in coordinate space as a function of the radial variable r does not emerge due to a compensating behaviour as r -> infty. Though in the short distance limit a dipole behaviour is present. We also demonstrate enhancement in the propagator of the bosonic localizing Zwanziger ghost field when the one loop Gribov gap equation is satisfied. The explicit form of the one loop gap equation for the Gribov mass parameter is also computed in the MOM scheme and the zero momentum value of the renormalization group invariant effective coupling constant is shown to be the same value as that in the MSbar scheme.Comment: 54 latex pages, 6 figures, flaw in original Feynman rules corrected with updated two loop gap equation; new details added on derivation of propagators and their one loop corrections as well as bosonic ghost enhancemen

Integrable Wilson loops

The generalized quark-antiquark potential of N=4 supersymmetric Yang-Mills theory on S^3 x R calculates the potential between a pair of heavy charged particles separated by an arbitrary angle on S^3 and also an angle in flavor space. It can be calculated by a Wilson loop following a prescribed path and couplings, or after a conformal transformation, by a cusped Wilson loop in flat space, hence also generalizing the usual concept of the cusp anomalous dimension. In AdS_5 x S^5 this is calculated by an infinite open string. I present here an open spin-chain model which calculates the spectrum of excitations of such open strings. In the dual gauge theory these are cusped Wilson loops with extra operator insertions at the cusp. The boundaries of the spin-chain introduce a non-trivial reflection phase and break the bulk symmetry down to a single copy of psu(2|2). The dependence on the two angles is captured by the two embeddings of this algebra into \psu(2|2)^2, i.e., by a global rotation. The exact answer to this problem is conjectured to be given by solutions to a set of twisted boundary thermodynamic Bethe ansatz integral equations. In particular the generalized quark-antiquark potential or cusp anomalous dimension is recovered by calculating the ground state energy of the minimal length spin-chain, with no sites. It gets contributions only from virtual particles reflecting off the boundaries. I reproduce from this calculation some known weak coupling perturtbative results.Comment: 40 pages, 11 figures; v2-some formulas corrected, results unchange