The spectral curve of segmented strings

Abstract: In this talk, I will discuss how to compute the spectral curve of ``segmented strings'' in AdS_3. The motion of a 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. Next, 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 mutation dynamics of a certain brane tiling. This will enable us to compute the spectral curve by taking the determinant of the dressed adjacency matrix of the tiling.

HEP - theorymathematical physicsexactly solvable and integrable systems

Audience: researchers in the topic

London Integrability Journal Club

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