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arXiv · 2112.14619

Segmented strings, brane tilings, and the Y-system

David Vegh
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Abstract

I show that the motion of a closed string consisting of $n$ segments in AdS$_3$ can be embedded into the mutation dynamics of the $Y^{n,0}$ brane tiling. The determinant of the Kasteleyn matrix computes the spectral curve. The dynamics is governed by a Y-system with additional constraints ensuring that the string closes in target space. The constraints can be deformed by coupling the worldsheet to a background two-form whose field strength is proportional to the volume form.

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David Vegh. 2021-12-29. Segmented strings, brane tilings, and the Y-system. https://arxiv.org/abs/2112.14619

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