Segmented strings from a different angle
David Vegh

TL;DR
This paper introduces a novel discretization of segmented strings in AdS$_3$, linking their geometry to integrable Toda-type lattices and providing exact solutions and energy calculations.
Contribution
It generalizes segmented strings to AdS$_3$, showing their relation to integrable lattices and deriving exact area and energy formulas.
Findings
Exact discretization of string equations of motion in AdS$_3$
Expression of string area via cross-ratios and kink variables
Reduction to integrable Toda-type lattice equations
Abstract
Segmented strings in flat space are piecewise linear classical string solutions. Kinks between the segments move with the speed of light and their worldlines form a lattice on the worldsheet. This idea can be generalized to AdS where the embedding is built from AdS patches. The construction provides an exact discretization of the non-linear string equations of motion. This paper computes the area of segmented strings using cross-ratios constructed from the kink vectors. The cross-ratios can be expressed in terms of either left-handed or right-handed variables. The string equation of motion in AdS is reduced to that of an integrable time-discretized relativistic Toda-type lattice. Positive solutions yield string embeddings that are unique up to global transformations. In the appendix, the Poincare target space energy is computed by integrating the worldsheet current along…
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Nonlinear Waves and Solitons · Computational Physics and Python Applications
