All-genus calculation of Wilson loops using D-branes

Abstract

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 α ′ . The resulting expression is in remarkable agreement with that found from a zero dimensional Gaussian matrix model.

On the integrability of Wilson loops inAdS5×S5: some periodic ansatze

“…In that case summing up the perturbative series (assuming no interactions) leads exactly to the string result including all non-planar corrections [14,15,16]. The agreement seems to hold for both the expectation value of the Wilson loop, as well as the correlation function of the Wilson loop with some local operators [17,18].…”

Semi-classical open string corrections and symmetric Wilson loops

“…It is convenient to use the coordinate system of [4]. The metric of AdS 5 is expressed as ds 2 = L 2 sin 2 η dη 2 + cos 2 ηdψ 2 + dρ 2 + sinh 2 ρ(dθ 2 + sin 2 θdφ) ,…”

“…The Wilson loop in the fundamental representation corresponds to a macroscopic fundamental string in AdS 5 × S 5 spacetime [2,3]. Moreover the Wilson loops in higher rank representations were recently explored in the AdS/CFT correspondence, the D-brane probe descriptions [2,4,5,6,7,8,9,10,11,12,13,14,15,16,17] and the supergravity descriptions [18,19] were developed.…”

“…One of these D-brane probe pictures is the D3-brane description of the symmetric or multiply wound Wilson loop [4]. These two different kind of Wilson loop (the multiply wound Wilson loop and symmetric one) have the same leading term in the expectation value in large λ ('t Hooft coupling) limit.…”

Non-abelian (p,q) strings in the warped deformed conifold

“…This prescription implies the following definition for the physical radius of the fuzzy sphere 22) where the quadratic Casimir is nowĈI q = (q 2 − 1)I q = n(n + 2)I n+1 in terms of the spin representation.…”