Embedding integrable superspin chain in string theory
Using results on topological line defects of 4D Chern-Simons theory and the algebra/cycle homology correspondence in complex surfaces S with ADE singularities, we study the graded properties of the sl(m|n) chain and its embedding in string theory. Because of the Z2-grading of sl(m|n), we show that t...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-05-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321323000858 |
| Summary: | Using results on topological line defects of 4D Chern-Simons theory and the algebra/cycle homology correspondence in complex surfaces S with ADE singularities, we study the graded properties of the sl(m|n) chain and its embedding in string theory. Because of the Z2-grading of sl(m|n), we show that the (m+n)!/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 Σg. 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 aspects like graded complex surfaces with sl(m|n) singularity as well as super magnons are also described. |
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| ISSN: | 0550-3213 |