Tuesday, May 3
11:00 AM -
12:00 PM EDT
Room 5209

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An introduction to segmented strings
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David Vegh
Queen Mary University of London

Host: Vladimir Rosenhaus

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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 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 an integrable model, the “spectral curve” encodes the information about the conserved charges of the solution. 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.

I discuss the simplest case in some detail: the closed string formed by four connected segments. A limiting case of this configuration is the yo-yo string whose motion is restricted to a 2d subspace. I describe its two-dimensional phase space and comment on quantization.