Portraits of the flux tube in QED3: A Monte Carlo simulation with external sources

We determine numerically, and display graphically, the electromagnetic energy distribution due to static sources in compact QED₃. Using the polymer formulation of the functional integral, Monte Carlo simulations are performed with external sources included in the lattice action. Both the Wilson and Villain forms of the action are studied, and the string tension is determined in a small range of weak couplings. For the Villain action, our values for the string tension σ are in agreement with Polyakov's formula. For the Wilson action, we are able to detect a string tension in a range of weak couplings 2.1 ? β ? 2.3 below the weak-to-strong coupling cross-over point. In the same range, standard Monte Carlo results for up to 8 × 8 Wilson loops are consistent with ordinary perturation theory (no confinement). A possible explanation of this discrepancy is discussed, and it is suggested that the standard (source-free) Monte Carlo might miss configurations which are important for flux-tube formation.     

Homology and abelian lattice gauge theories

A simple Abelian model with both Higgs and gauge field degrees of freedom is investigated on a simplicial lattice of arbitrary dimension. We use group character expansion for both fields to get a diagrammatic expansion of the partition function. The diagrams consist of gauge group representation valued 1- and 2-chains. The diagrams are proved to satisfy the constraint that the boundary of the 2-chain representing the gauge field is equal to the 1-chain representing the Higgs field. Otherwise they identically vanish. Simple consequences of this are current conservation and the vanishing of non-null-homologous Wilson loops. Finally we use this picture for giving a lowest order estimate for the critical length of a string. This is the length at which the flux-tube string connecting two opposite charges is likely to break into two pieces due to pair creation.     

Three-dimensional lattice gauge theory and strings

We consider SU(2) lattice gauge theory in three dimensions. The Wilson loops are found to be well described by a simple string model in the approximate scaling region.     

Renormalization of loop functions in QCD

We give a short overview of the renormalization properties of rectangular Wilson loops, the Polyakov loop correlator and the cyclic Wilson loop. We then discuss how to renormalize loops with more than one intersection, using the simplest non-trivial case as an illustrative example. Our findings expand on previous treatments. The generalized exponentiation theorem is applied to the Polyakov loop correlator and used to renormalize linear divergences in the cyclic Wilson loop.     

Semiclassical correlation functions of Wilson loops and local vertex operators

We analyze correlation functions of Wilson loop observables and local vertex operators within the strong-coupling regime of the AdS/CFT correspondence. When the local operator corresponds to a light string state with finite conserved charges the correlation function can be evaluated in the semiclassical approximation of large string tension, where the contribution from the light vertex can be neglected. We consider the cases where the Wilson loops are described by two concentric surfaces and the local vertices are the superconformal chiral primary scalar or a singlet massive scalar operator.     

On the ground state of Yang–Mills theory

We investigate the overlap of the ground state meson potential with sets of mesonic-trial wave functions corresponding to different gluonic distributions. We probe the transverse structure of the flux tube through the creation of non-uniform smearing profiles for the string of glue connecting two color sources in Wilson loop operator. The non-uniformly UV-regulated flux-tube operators are found to optimize the overlap with the ground state and display interesting features in the ground state overlap.     

Planar and non-planar Wilson loops in QCD

A general QCD sum rule calculation of vacuum expectation values of Wilson loops is presented and particularized to several specific planar and non-planar contours. The string tension obtained is √σ = 0.50(5) GeV. Within the errors of the approach, this result is shape-independent. We comment on the possibility that corrections to the area and perimeter laws could be parametrized by a geodesic curvature term.     

Supersymmetric Wilson loops in super-Chern–Simons-matter theory

We study supersymmetric Wilson loop operators in ABJM theory from both sides of the AdS₄/CFT₃ correspondence. We first construct some supersymmetric Wilson loops. The perturbative computations are performed in the field theory side at the first two orders. A fundamental string solution ending on a circular loop is also studied.     

Wilson loops T-dual to short strings

We show that closed string solutions in the bulk of AdS space are related by T-duality to solutions representing an open string ending at the boundary of AdS. By combining the limit in which a closed string becomes small with a large boost, we find that the near-flat space short string in the bulk maps to a periodic open string world surface ending on a wavy line at the boundary. This open string solution was previously found by Mikhailov and corresponds to a time-like near-BPS Wilson loop differing by small fluctuations from a straight line. A simple relation is found between the shape of the Wilson loop and the shape of the closed string at the moment when it crosses the horizon of the Poincaré patch. As a result, the energy and spin of the closed string are encoded in properties of the Wilson loop. This suggests that closed string amplitudes with one of the closed strings falling into the Poincaré horizon should be dual to gauge theory correlators involving local operators and a Wilson loop of the T-dual (“momentum”) theory.     

U(3) four-dimensional lattice gauge theory and Monte Carlo calculations

Monte Carlo results for the pure U(3) lattice gauge theory on a 6⁴ lattice are reported. Wilson loops and the string tension are presented. The first-order phase transition in U(3) is reflected quite clearly in a discontinuity in the string tension at β = β_c. The U(1) factor of U(3) is extracted using the determinant of the Wilson loops. As expected, the U(1) component appears to deconfine at the phase transition..     

Rotating dyonic dipole black rings: exact solutions and thermodynamics

New rotating dyonic dipole black ring solutions are derived in 5D Einstein-dilaton gravity with antisymmetric forms. The black rings are analyzed and their thermodynamics is discussed. New dyonic black string solutions are also presented.     

Wilson loops in warped resolved deformed conifolds

We calculate quark–antiquark potentials using the relationship between the expectation value of the Wilson loop and the action of a probe string in the string dual. We review and categorise the possible forms of the dependence of the energy on the separation between the quarks. In particular, we examine the possibility of there being a minimum separation for probe strings which do not penetrate close to the origin of the bulk space, and derive a condition which determines whether this is the case. We then apply these considerations to the flavoured resolved deformed conifold background of Gaillard et al. (2010) [8]. We suggest that the unusual behaviour that we observe in this solution is likely to be related to the IR singularity which is not present in the unflavoured case.     

Wilson loops in 3<Emphasis Type="Italic">d</Emphasis> QFT from D-branes in AdS<Subscript>4</Subscript>×CP<Superscript>3</Superscript>

We study the Wilson loops in three-dimensional QFT from the D-branes in the AdS₄×CP³ geometry. We find explicit D-brane configurations in the bulk which correspond to both straight and circular Wilson lines extended to the boundary of AdS₄. We analyze critically the role of boundary contributions to the D2-branes with various topology and fundamental string actions.     

Topological Field Theory Interpretation of String Topology

The string bracket introduced by Chas and Sullivan is reinterpreted from the point of view of topological field theories in the Batalin–Vilkovisky or BRST formalisms. Namely, topological action functionals for gauge fields (generalizing Chern–Simons and BF theories) are considered together with generalized Wilson loops. The latter generate a (Poisson or Gerstenhaber) algebra of functionals with values in the S¹-equivariant cohomology of the loop space of the manifold on which the theory is defined. It is proved that, in the case of GL(n,) with standard representation, the (Poisson or BV) bracket of two generalized Wilson loops applied to two cycles is the same as the generalized Wilson loop applied to the string bracket of the cycles. Generalizations to other groups are briefly described.     

Wilson loops on 324 lattices and theSU(3) potential

Wilson loops are calculated on 32⁴ lattices in the coupling regime 6/g ²=6.3–6.9. Determination of the string tension from these loops with a method based on string model calculations shows a string tension that does not seem to scale. This is probably due to the amount of statistics. It points to difficulties in obtaining accurate physical results for coupling values above 6.6. Suggestions to improve this situation are made.     

Grand unified strings and galaxy formation

The possibility that topologically stable strings formed at a grand unification phase transition led to galaxy formation is discussed. A large class of solutions describing non-self-intersecting loops is presented. The gravitational field and power radiated from a simple class of oscillating configurations of string is calculated, and the possibility of its detection discussed. Unique features of the string scenario are emphasized.     

Numerical analysis of the twisted Eguchi-Kawai model in four dimensions

We perform a high statistics Monte Carlo calculation of the string tension in the twisted SU(N) Eguchi-Kawai model for N=36 and N=64. The string tension, calculated from Wilson loops not larger than 3 × 3, clearly shows the renormalization group scaling behaviour.