Wilson loops in Script N = 4 SYM and fermion droplets

Abstract

The matrix models which are conjectured to compute the circle Wilson loop and its correlator with chiral primary operators are mapped onto normal matrix models. A fermion droplet picture analogous to the well-known one for chiral primary operators is shown to emerge in the large N limit. Several examples are computed. We find an interesting selection rule for the correlator of a single trace Wilson loop with a chiral primary operator. It can be non-zero only if the chiral primary is in a representation with a single hook. We show that the expectation value of the Wilson loop in a large representation labelled by a Young diagram with a single row has a first order phase transition between a regime where it is identical to a large column representation and a regime where it is a large wrapping number single trace Wilson loop.

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

“…Another recent development in the study of Wilson loops is the renewed interest in the description of them in terms of D-branes [3,14,15,[23][24][25]. It would be very interesting to find the relevant solutions for the 1/4 BPS Wilson loops, see if there are two solutions also for the DBI action, and study the 1/N corrections to the two saddle points.…”

Higher rank Wilson loops in N = 2∗ super-Yang-Mills theory

“…Wilson loops of rank k ∼ N are dual to D-brane configurations carrying the fundamental string charge [18][19][20][21][22][23][24], and have been extensively studied in the N = 4 super-Yang-Mills theory [19,23,[25][26][27][28][29][30], for which the matrix model is just Gaussian [31,32]. As far as N = 2 theories are concerned, higher-rank Wilson loops have been calculated for the N = 2 superconformal QCD [33], whose solution at strong coupling is known [34] but is very different from that of SYM*.…”

Higher rank Wilson loops from a matrix model

“…Wilson lines provide another family of half BPS operators and so it is natural to search for a bubbling geometry formalism describing the backreaction of the D3 and D5 branes, as well as a field theory understanding in terms of fermion droplets. Exciting progress in this direction is currently being made [16][17][18]. This line of interest inspired the succesful matching of a bulk D5 brane computation with a matrix model computation of the rank k antisymmetric Wilson loop [19].…”