All-genus calculation of Wilson loops using D-branes

By N. Drukker, B. Fiol. 2005

344 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/28c1fa6ad3c152450c241e7b27a44b9470396919

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In Geometry and Topology

1. N. Drukker
2. Pavel Putrov
3. S. Hartnoll
4. S. Kumar
5. S. Giombi
6. R. Roiban
7. J. Maldacena
8. Joaquim Gomis

In Nuclear and High Energy Physics

1. N. Drukker
2. J. Maldacena
3. Marcos Mariño
4. A. Tseytlin
5. R. Roiban
6. Aitor Lewkowycz
7. S. Frolov
8. Pavel Putrov

In Statistical and Nonlinear Physics

1. Marcos Mariño
2. N. Drukker
3. J. Maldacena
4. Aitor Lewkowycz
5. Pavel Putrov
6. V. Hubeny
7. S. Hartnoll
8. O. Lunin

Citations in the corpus

• Holographic Wilson loops (2006, background): “The classical equations of motion of a D3-brane with an AdS2×S(2) geometry and with k fundamental strings dissolved in it (which we label by D3k) has been studied recently by Drukker and Fiol [7].”
• 1/4 BPS circular loops, unstable world-sheet instantons and the matrix model (2006, background): “(2)For some results beyond the planar level see [14, 15] (3)Those saddle points come from the semiclassical evaluation of the integral in (4.”
• Wilson Loops as D3-Branes (2006, background): “We can now make contact with theD3k-brane solution [4][2] in AdS5×S(5).”
• Higher rank Wilson loops from a matrix model (2006, methodology): “(2.42) Plugging this back into (2.39) we obtain the contribution to the Wilson loop from this saddle point as W1 = exp [ 2N ( κ √ 1 + κ2 + sinh−1 κ )] , (2.43) which is exactly the result found by Drukker and Fiol [13] using a probe D3 brane in AdS5 × S5.”
• Supersymmetric Wilson loops on S**3. (2007, methodology): “8) can be matched against the classical action of a string worldsheet in AdS, and certain 1/N corrections were also correctly reproduced by D-branes corresponding to Wilson loops in large representations of the gauge group [12, 14, 15].”
• Wilson loops in 3-dimensional N=6 supersymmetric Chern-Simons Theory and their string theory duals (2008, background): “Such a prescription indeed gave the correct result in N = 4 SYM in four dimensions [29](3).”
• Wilson Loops of Anti-symmetric Representation and D5-branes (2006, methodology): “2 Supersymmetry of the AdS2 × S2 D3-branes Let us first consider here the supersymmetry preserved by an AdS2 × S2 D3-brane of [3] in order to compare it to the one preserved by a D5-brane.”
• Small deformations of supersymmetric Wilson loops and open spin-chains (2006, background): “While there are a lot of interesting results for the simple circular loop [29,30,16], we wish to consider more general operators but still limit ourselves to operators close to the symmetric ones.”
• On gravitational description of Wilson lines (2006, background): “4) According to the proposal of [11, 18], a dual description of the Wilson line is given by a D3 brane with worldvolume AdS2 × S(2), which is symmetric under SO(5) rotations and has an electric field along its worldvolume.”
• Half-BPS Wilson loop and AdS2/CFT1 (2017, background): “5 One may also consider the D3 and D5 branes dual to 1/2-BPS Wilson loops in higher-rank symmetric and antisymmetric representations [32,33,15,34]: these branes have AdS2 × S2 or AdS2 × S4 worldvolumes, and preserve the same OSp(4∗|4) symmetry as the fundamental string.”
• Exact results for the entanglement entropy and the energy radiated by a quark (2013, methodology): “We can compute the entanglement entropy for the k-symmmetric and k-antisymmetric representations at strong coupling [38, 39, 40] for k,N →∞ and k/N =fixed.”
• The AdS/CFT correspondence (2014, background): “27 In fact, certain other representations can be better characterized using D3-branes, and hence by corresponding three-dimensional extremal surfaces [48] (though in even more exotic cases, with sufficiently many such branes, the bulk is better described by regular but topologically non-trivial ‘bub”
• BUBBLING GEOMETRIES FOR HALF-BPS WILSON LINES (2006, methodology): “As a father check, we compare an AdS2 × S(2) D3-brane probe of [3] and the eigenvalue distribution of the saddle point of the integral 〈 1 N tr[e ] 〉 mm in the matrix model.”
• From Weak to Strong Coupling in ABJM Theory (2010, background): “We will now discuss the expansion of the result for the giant Wilson loop for large κ , since this is the strong coupling limit in which one makes contact with the AdS geometry [33].”