Embedding Integrable Superspin Chain in String Theory

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.

LaTeX, 60 pages, 18 figures

References in corpus (3)

• The algebra of Wilson-'t Hooft operators
• D-string fluid in conifold: I. Topological gauge model
• Lax Operator and superspin chains from 4D CS gauge theory