Nonlocal Symmetries, Spectral Parameter and Minimal Surfaces in AdS/CFT

Abstract

We give a general account of nonlocal symmetries in symmetric space models and their relation to the AdS/CFT correspondence. In particular, we study a master symmetry which generates the spectral parameter and acts as a level-raising operator on the classical Yangian generators. The master symmetry extends to an infinite tower of symmetries with nonlocal Casimir elements as associated conserved charges. We discuss the algebraic properties of these symmetries and establish their role in explaining the recently observed one-parameter deformation of holographic Wilson loops. Finally, we provide a numerical framework, in which discretized minimal surfaces and their master symmetry deformation can be calculated.

50 pages, 8 figures, v2: minor changes, published version, v3: signs in (B.16) and (5.8) and coefficients in (5.12) corrected, footnote 4 added

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Cited by in corpus (8)

• Yangian Symmetry of String Theory on $Ad{S}_3\times S^3\times S^3\times S^1$ with Mixed 3-form Flux
• Deformations of the circular Wilson loop and spectral (in)dependence
• $q$-Poincaré supersymmetry in $Ad{S}_5/CF{T}_4$
• Minimal area surfaces in AdS_{n+1} and Wilson loops
• $q$-Poincaré invariance of the $Ad{S}_3/CF{T}_2$ $R$-matrix
• Dual conformal transformations of smooth holographic Wilson loops
• Minimal area surfaces in AdS${}_3$ through integrability
• Wilson Loops and Integrability