Wilson Loops and Minimal Surfaces

Abstract

The AdS/CFT correspondence suggests that the Wilson loop of the large N gauge theory with N=4 supersymmetry in 4 dimensions is described by a minimal surface in AdS_5 x S^5. We examine various aspects of this proposal, comparing gauge theory expectations with computations of minimal surfaces. There is a distinguished class of loops, which we call BPS loops, whose expectation values are free from ultra-violet divergence. We formulate the loop equation for such loops. To the extent that we have checked, the minimal surface in AdS_5 x S^5 gives a solution of the equation. We also discuss the zig-zag symmetry of the loop operator. In the N=4 gauge theory, we expect the zig-zag symmetry to hold when the loop does not couple the scalar fields in the supermultiplet. We will show how this is realized for the minimal surface.

51 pages, 7 figures

References in corpus (1)

• Improved heavy quark potential at finite temperature from anti-de Sitter supergravity

Cited by in corpus (355)

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• Correlators of Circular Wilson Loops from Holography
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• Minimal area surfaces in AdS${}_3$ through integrability
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• The quark-gluon plasma and D6-branes on the conifold
• Topics in Cusped/Lightcone Wilson Loops
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• T-duality to Scattering Amplitude and Wilson Loop in Non-commutative Super Yang-Mills Theory
• The AdS/CFT Correspondence: Classical, Quantum, and Thermodynamical Aspects
• Generalised cusp anomalous dimension in beta-deformed super Yang Mills theory
• Holographic repulsion and confinement in gauge theory
• On disc-with-hole and disc-with-handle partition functions in bosonic string theory
• Worldsheets in Holography: Computing Corrections to the Veneziano Amplitude
• Universal sectors in superconformal defects
• Schwinger Type Pair Production in Non-SUSY AdS/CFT
• Entanglement and Excitations in Gauge/Gravity Duality
• Beyond AdS${}_2$/dCFT${}_1$: Insertions in Two Wilson Loops
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• Supersymmetric String Configurations in Ad${\mathbb{S}}_5\times {\mathbb{S}}^5$
• Confining strings, Wilson loops and extra dimensions
• Holographic Wilson Loop One-point Functions in ABJM Theory
• D-branes, gauge/string duality and noncommutative theories
• Note About String with Euclidean World-Sheet in AdS(5)xS(5)
• String Theory and Turbulence
• Confinement of N=1 Super Yang-Mills from Supergravity