Abstract
This paper describes the motion of a classical Nambu-Goto string in three-dimensional anti-de Sitter spacetime in terms of two ‘celestial’ fields on the worldsheet. The fields correspond to retarded and advanced boundary times at which null rays emanating from the string reach the boundary. The formalism allows for a simple derivation of the Schwarzian action for near-AdS2 embeddings.
Highlights
By non-linear equations and they provide a simple laboratory for studying non-linear phenomena such as wave turbulence and energy cascades [1, 2]
This paper describes the motion of a classical Nambu-Goto string in threedimensional anti-de Sitter spacetime in terms of two ‘celestial’ fields on the worldsheet
A long string on the gravity side ending on the boundary is nothing but the dual of a flux tube stretching between external quarks in the boundary field theory
Summary
Three-dimensional anti-de Sitter spacetime can be immersed into the R2,2 linear ambient space. AdS is the universal cover of the hyperboloid. Global AdS time is the angle on the Y−1, Y0 plane. A part of global AdS3 is covered by the Poincaré patch. In terms of the Y coordinate, the boundary is the set of points that satisfy Y 2 = 0 with the identification Y ∼= cY (where c ∈ R+). The string can be mapped into AdS3 by first taking the target space to be R2,2 and forcing the string to lie on the hyperboloid (2.1) by means of a Lagrange multiplier λ. Due to the gauge choice, the equations are supplemented by the constraints.
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