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.

arXiv commentLaTeX, 60 pages, 18 figures

References in corpus (26)

• Supersymmetric vacua and Bethe ansatz
• Wilson-'t Hooft operators in four-dimensional gauge theories and S-duality
• Quantum integrability and supersymmetric vacua
• The Omega Deformation, Branes, Integrability, and Liouville Theory
• Discovery of coexisting Dirac and triply degenerate magnons in a three-dimensional antiferromagnet
• String theory of the Omega deformation
• Borcherds symmetries in M-theory
• The Omega Deformation From String and M-Theory
• The algebra of Wilson-'t Hooft operators
• Geometric Engineering of N=2 CFT_{4}s based on Indefinite Singularities: Hyperbolic Case
• RG Cascades in Hyperbolic Quiver Gauge Theories
• String hypothesis for gl(n|m) spin chains: a particle/hole democracy
• Topological Holography: The Example of The D2-D4 Brane System
• Feynman diagrams and $\Omega$-deformed M-theory
• Explicit Analysis of Kahler Deformations in 4D N=1 Supersymmetric Quiver Theories
• D-string fluid in conifold: I. Topological gauge model
• 't Hooft lines of ADE-type and Topological Quivers
• HyperKhaler Metrics Building and Integrable Models
• Wilson-'t Hooft lines as transfer matrices
• Quantum line operators from Lax pairs
• ABCD of 't Hooft operators
• Little String Origin of Surface Defects
• Lax Operator and superspin chains from 4D CS gauge theory
• Unifying Lattice Models, Links and Quantum Geometric Langlands via Branes in String Theory
• Weak Coupling Chambers in N=2 BPS Quiver Theory
• Mutation Symmetries in BPS Quiver Theories: Building the BPS Spectra

Cited by in corpus (6)

• 't Hooft lines of ADE-type and Topological Quivers
• Finiteness of 3D higher spin gravity Landscape
• Superspin Chains Solutions from 4D Chern-Simons Theory
• Topological 4D gravity and gravitational defects
• Code CFTs and Topological Matter
• Elliptic Stable Envelopes for Certain Non-Symplectic Varieties and Dynamical $R$-Matrices for Superspin Chains from the Bethe/Gauge Correspondence