1/4 BPS circular loops, unstable world-sheet instantons and the matrix model

The standard prescription for computing Wilson loops in the AdS/CFT correspondence in the large coupling regime and tree-level involves minimizing the string action. In many cases the action has more than one saddle point as in the simple example studied in this paper, where there are two 1/4 BPS string solutions, one a minimum and the other not. Like in the case of the regular circular loop the perturbative expansion seems to be captured by a free matrix model. This gives enough analytic control to extrapolate from weak to strong coupling and find both saddle points in the asymptotic expansion of the matrix model. The calculation also suggests a new BMN-like limit for nearly BPS Wilson loop operators.Comment: 13 pages, amste

Wilson Loops as Matrix Strings

In the framework of Matrix theory we show that Wilson loops can serve as interpolating fields to define string scattering amplitudes as gauge theory observables.Comment: 5 pages, LaTeX, reference adde

The N=4{\cal N}=4 Schur index with Polyakov loops

Recently the Schur index of ${\cal N}=4$ SYM was evaluated in closed form to all orders including exponential corrections in the large $N$ expansion and for fixed finite $N$. This was achieved by identifying the matrix model which calculates the index with the partition function of a system of free fermions on a circle. The index can be enriched by the inclusion of loop operators and the case of Wilson loops is particularly easy, as it amounts to inserting extra characters into the matrix model. The Fermi-gas approach is applied here to this problem, the formalism is explored and explicit results at large $N$ are found for the fundamental as well as a few other symmetric and antisymmetric representations.Comment: 15 pages. 1 figur

Dressed Wilson loops on S-2

archiveprefix: arXiv primaryclass: hep-th reportnumber: HU-EP-11-19 slaccitation: %%CITATION = ARXIV:1104.3746;%%archiveprefix: arXiv primaryclass: hep-th reportnumber: HU-EP-11-19 slaccitation: %%CITATION = ARXIV:1104.3746;%%CK has been supported by Deutsche Forschungsgemeinschaft via SFB 647. DY was supported by FNU through grant number 272-08-0329

D-brane Description of New Open String Solutions in AdS(5)

In this paper we find D-brane descriptions of some of new open string solutions that were found in 0804.3438[hep-th]. These D5-brane and D3-brane configurations give gravitational dual descriptions of Wilson loops in some particular representations.Comment: 13 pages, references adde

Supersymmetric Wilson Loops in N=6 Super Chern-Simons-matter theory

We study supersymmetric Wilson loop operators in ABJM theory from both sides of the AdS_4/CFT_3 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.Comment: 21 pages, 6 figures; v2: minor changes; v3, 21 pages, 4 figures, major revisions, published versio

A Semiclassical String Description of Wilson Loop with Local Operators

We discuss a semiclassical string description to circular Wilson loops without/with local operator insertions. By considering a semiclassical approximation of type IIB string theory on AdS_5 X S^5 around the corresponding classical solutions, quadratic actions with respect to fluctuations are computed. Then the dual corresponding operators describing the fluctuations are discussed from the point of view of a small deformation of the Wilson loops. The result gives new evidence for AdS/CFT correspondence.Comment: 23pp, 1 figure; typos fixed, version to be published in NP

3d mirror symmetry as a canonical transformation

We generalize the free Fermi-gas formulation of certain 3d ${\cal N}=3$ supersymmetric Chern-Simons-matter theories by allowing Fayet-Iliopoulos couplings as well as mass terms for bifundamental matter fields. The resulting partition functions are given by simple modifications of the argument of the Airy function found previously. With these extra parameters it is easy to see that mirror-symmetry corresponds to linear canonical transformations on the phase space (or operator algebra) of the 1-dimensional fermions.Comment: 11 pages, 2 figures. v2: figure added - version published in JHE

All-genus calculation of Wilson loops using D-branes

The standard prescription for calculating a Wilson loop in the AdS/CFT correspondence is by a string world-sheet ending along the loop at the boundary of AdS. For a multiply wrapped Wilson loop this leads to many coincident strings, which may interact among themselves. In such cases a better description of the system is in terms of a D3-brane carrying electric flux. We find such solutions for the single straight line and the circular loop. The action agrees with the string calculation at small coupling and in addition captures all the higher genus corrections at leading order in alpha'. The resulting expression is in remarkable agreement with that found from a zero dimensional Gaussian matrix model.Comment: 29 pages, LeTeX, one colour figure. v2: citation corrected. v3: minor typ