Journal of Statistical Physics

, Volume 156, Issue 6, pp 1199–1220 | Cite as

Dynamic Lattice Supersymmetry in \(\mathfrak {gl}\left( {n}|{m}\right) \) Spin Chains



Supersymmetry operators that change a spin chain’s length have appeared in numerous contexts, ranging from the AdS/CFT correspondence to statistical mechanics models. In this article, we present, via an analysis of the Bethe equations, all homogeneous, rational and trigonometric, integrable \(\mathfrak {gl}( n|m)\) spin chains for which length-changing supersymmetry can be present. Furthermore, we write down the supercharges explicitly for the simplest new models, namely the \(\mathfrak {sl}( n|1)\) spin chains with the \((n-1)\)-fold antisymmetric tensor product of the fundamental representation at each site and check their compatibility with integrability.


Supersymmetry Spin chains Integrable models 



The authors thank Rouven Frassek, Sergey Frolov, Nils Kanning, Yumi Ko, Matthias Staudacher, Zengo Tsuboi, Matthias Wilhelm and especially Christian Hagendorf for inspiring discussions and insightful suggestions. Furthermore VM is grateful to the Kavli IPMU, Université Catholique de Louvain and Sogang University for the kind hospitality while working on parts of the manuscript.


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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institut für Mathematik und Institut für PhysikHumboldt-Universität zu BerlinBerlinGermany

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