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arXiv · 2304.03152

Embedding Integrable Superspin Chain in String Theory

Y. Boujakhrout·E. H Saidi·R. Ahl Laamara·L. B Drissi
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Abstract

Using results on topological line defects of 4D Chern-Simons theory and the algebra/cycle homology correspondence in complex surfaces $\mathcal{S}$ with ADE singularities, we study the graded properties of the $sl(m|n)$ chain and its embedding in string theory. Because of the $\mathbb{Z}_{2}$-grading of $ sl(m|n)$, we show that the $\left( m+n\right) !/m!n!$ varieties of superspin chains with underlying super geometries have different cycle homologies. We investigate the algebraic and homological features of these integrable quantum chains and give a link between graded 2-cycles and genus-g Rieman surfaces $\Sigma _{g}$. Moreover, using homology language, we yield the brane realisation of the $sl(m|n)$ chain in type IIA string and its uplift to M-theory. Other \textrm{aspects} like graded complex surfaces with $sl(m|n)$ singularity as well as super magnons are also described.

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Y. Boujakhrout, E. H Saidi, R. Ahl Laamara, L. B Drissi. 2023-04-06. Embedding Integrable Superspin Chain in String Theory. https://doi.org/10.1016/j.nuclphysb.2023.116156

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