Wilson Loops in N=4 Supersymmetric Yang--Mills Theory

By J. Erickson, G. Semenoff, K. Zarembo. 2000

673 citations recorded by the source corpus.

Perturbative computations of the expectation value of the Wilson loop in N=4 supersymmetric Yang-Mills theory are reported. For the two special cases of a circular loop and a pair of anti-parallel lines, it is shown that the sum of an infinite class of ladder-like planar diagrams, when extrapolated to strong coupling, produces an expectation value characteristic of the results of the AdS/CFT correspondence, $ \sim\exp((constant)\sqrt{g^2N})$. For the case of the circular loop, the sum is obtained analytically for all values of the coupling. In this case, the constant factor in front of $\sqrt{g^2N}$ also agrees with the supergravity results. We speculate that the sum of diagrams without internal vertices is exact and support this conjecture by showing that the leading corrections to the ladder diagrams cancel identically in four dimensions. We also show that, for arbitrary smooth loops, the ultraviolet divergences cancel to order $g^4N^2$.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/5c565a467b2188aafc2087907eea79f7b7dd3095

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

1. N. Drukker
2. A. Tseytlin
3. J. Maldacena
4. N. Beisert
5. S. Frolov
6. Marcos Mariño
7. R. Roiban
8. S. Giombi

Citations in the corpus

• Three-dimensional N=6 SCFT's and their membrane dynamics (2008, background): “The setup is similar to what has been done for N = 4 SYM before.”
• Operators with Large R-Charge in N=4 Yang-Mills Theory (2002, methodology): “theory for N = 4 Yang-Mills in the context of the AdS/CFT correspondence. In particular, a remarkable computation of the circular Wilson loops to all orders in perturbation theory in was performed in [29]. A perturbative computation of the correlation functions of the BPS operators at two loop order”
• Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops (2007, neutral): “In [9] the conjecture was tested at oneloop level in gauge theory.”
• Exact results for the entanglement entropy and the energy radiated by a quark (2013, methodology): “Using localization [4, 31, 32] an exact expression for the loop was found”
• Half-BPS Wilson loop and AdS2/CFT1 (2017, background): “More generally, one should normalize the correlator on the right-hand side by the expectation value of the Wilson loop without insertions (this is relevant in the case of the 1/2-BPS circular loop, which has a non-trivial expectation value [6–8]).”
• Exact results in ABJM theory from topological strings (2009, methodology): “In retrospect, one could say that the result of [3, 2, 1] for the 1/4 BPS Wilson loop in N = 4 super Yang–Mills theory is comparatively easier since in their case the relevant matrix model is the Gaussian one, with a simpler moduli space, and where the ’t Hooft parameter is simply equal to the bare ”
• A semi-classical limit of the gauge/string correspondence (2002, background): “The successes [17, 16] in computing circular Wilson loops to all orders in the ’t Hooft coupling lead us to hope that similar exact resummations (perhaps of rainbow graphs) might lead to a direct comparison between strongly coupled field theory and string theory near the leading edge of the Regge tr”
• All-genus calculation of Wilson loops using D-branes (2005, background): “The combined propagator of the gauge field and scalar is a constant, which reduces the calculation of all rainbow/ladder diagrams to a zero-dimensional matrix model [17], which can be written explicitly as an integral over”
• Summing up all genus free energy of ABJM matrix model (2011, background): “However, there has been important progress in the localization technique in supersymmetric gauge theories [4], elucidating ealier works [5, 6].”
• A New Double-Scaling Limit of N = 4 Super Yang-Mills Theory and PP-Wave Strings (2002, methodology): “ce operators. When we work in 2ω-dimensions, the right-hand side of this equation should replace 1/4π2[x2] in propagators. Useful formulae for Feynman integrals in 2ω- dimensions can be found in refs.[10, 11]. 5.2 One-loop integrals The Feynman diagrams which contribute to radiative corrections to t”
• Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories (2011, background): “ will give a brief summary of more recent results along these lines. 9.1 Wilson loops and higher genus corrections One of the original goals of [76] was to use localization to prove the conjecture of [34, 28]. According to this conjecture, the vacuum expectation value of 1=2 BPS Wilson loops can be ”
• Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant (2012, methodology): “Such a technique was applied [20] to 4d N = 4 super Yang-Mills theory, and some conjecture on the half-BPS Wilson loops1 [21, 22] has been confirmed.”
• Supersymmetric gauge theories on the five-sphere (2012, background): “ considered in [3], where it was shown that the partition function as well as the expectation values of certain Wilson loops can be computed as certain matrix integrals which were first conjectured by [4, 5]. The e xact results also led to the discovery of a surprising relation between 4d N = 2 SUSY ”
• Generalized quark-antiquark potential at weak and strong coupling (2011, methodology): “Due to this fact, in the present circumstances the line and the circle are equivalent and we will not recover the matrix model describing the expectation value of the circle [5, 11, 12] in the θ = φ = 0 limit.”
• Holographic Wilson loops (2006, background): “It would also be interesting to consider the case of a circular Wilson loop(6) and study the defect field theory origin of the matrix model proposed by Erickson, Semenoff and Zarembo [12][13] for the study of circular Wilson 6 Which breaks a different set of supersymmetries compared to the loops con”
• Wilson loops in 3-dimensional N=6 supersymmetric Chern-Simons Theory and their string theory duals (2008, background): “In support of this identification we demonstrate that these string theory solutions match the symmetries, charges and the preserved supersymmetries of their Chern-Simons theory counterparts.”