Speaker
Description
In this talk, I will describe ``segmented strings'' moving in three-dimensional anti-de Sitter spacetime. The motion of a bosonic string in this target space is classically integrable and the worldsheet theory can be discretized while preserving integrability. The corresponding embeddings are segmented strings, which generalize piecewise linear strings in flat space. I will present several examples.
In order to compute the spectral curve of the string, I will introduce ``brane tilings'', which are doubly-periodic planar bipartite graphs. I will show that the motion of a closed segmented string can be embedded into the cluster transformation dynamics of a certain brane tiling. This will enable us to compute the spectral curve of the string by simply taking the determinant of the adjacency matrix of the tiling.
I discuss the simplest case in some detail: the closed string formed by four connected segments. A limiting case of this configuration is the folded string whose motion is restricted to a 2d subspace. I comment on quantization and the relationship to the 't Hooft equation, which describes meson bound states in two-dimensional planar QCD.
