Higher rank Wilson loops from a matrix model

Abstract

We compute the circular Wilson loop of N = 4 SYM theory at large N in the rank k symmetric and antisymmetric tensor representations. Using a quadratic Hermitian matrix model we obtain expressions for all values of the 't Hooft coupling. At large and small couplings we give explicit formulae and reproduce supergravity results from both D3 and D5 branes within a systematic framework.

Perturbative and Non-perturbative Approaches to String Sigma-Models in AdS/CFT

“…The matrix model of the circular loop is consistent with the AdS/CFT prediction as reproduced by string theory, namely the leading behaviour at large λ and N [374] and the behaviour at leading λ and all N −1 -corrections from D3-branes [376,377] and D5-branes [378,379].…”

Holographic lattices, dimers, and glasses

“…Turning it into the appropriate Euclidean configuration, the Euclidean action of the D5-brane is evaluated to be [26][27][28] …”

Weak coupling large-N transitions at finite baryon density

“…Possibly, Polyakov loops in rank k tensor representions, symmetric or antisymmetric, with k ∼ O(N ), could exhibit specific non-analyticities associated to the splitting of the distribution. Such observables are known to encode gapping transitions of the GrossWitten-Wadia (GWW) type [40], and can be computed using methods explicitly discussed in [41]. We postpone further study of these issues for future work.…”