dorsal/arxiv
View SchemaThe continuum limit of sl(N/K) integrable super spin chains
| Authors | H. Saleur |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9905007 |
| URL | https://arxiv.org/abs/solv-int/9905007 |
| DOI | 10.1016/S0550-3213(00)00002-X |
| Journal | Nucl.Phys. B578 (2000) 552-576 |
Abstract
I discuss in this paper the continuum limit of integrable spin chains based on the superalgebras sl(N/K). The general conclusion is that, with the full ``supersymmetry'', none of these models is relativistic. When the supersymmetry is broken by the generator of the sub u(1), Gross Neveu models of various types are obtained. For instance, in the case of sl(N/K) with a typical fermionic representation on every site, the continuum limit is the GN model with N colors and K flavors. In the case of sl(N/1) and atypical representations of spin j, a close cousin of the GN model with N colors, j flavors and flavor anisotropy is obtained. The Dynkin parameter associated with the fermionic root, while providing solutions to the Yang Baxter equation with a continuous parameter, thus does not give rise to any new physics in the field theory limit. These features are generalized to the case where an impurity is embedded in the system.
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"abstract": "I discuss in this paper the continuum limit of integrable spin chains based\non the superalgebras sl(N/K). The general conclusion is that, with the full\n``supersymmetry\u0027\u0027, none of these models is relativistic. When the supersymmetry\nis broken by the generator of the sub u(1), Gross Neveu models of various types\nare obtained. For instance, in the case of sl(N/K) with a typical fermionic\nrepresentation on every site, the continuum limit is the GN model with N colors\nand K flavors. In the case of sl(N/1) and atypical representations of spin j, a\nclose cousin of the GN model with N colors, j flavors and flavor anisotropy is\nobtained. The Dynkin parameter associated with the fermionic root, while\nproviding solutions to the Yang Baxter equation with a continuous parameter,\nthus does not give rise to any new physics in the field theory limit.\n These features are generalized to the case where an impurity is embedded in\nthe system.",
"arxiv_id": "solv-int/9905007",
"authors": [
"H. Saleur"
],
"categories": [
"solv-int",
"cond-mat",
"hep-th",
"nlin.SI"
],
"doi": "10.1016/S0550-3213(00)00002-X",
"journal_ref": "Nucl.Phys. B578 (2000) 552-576",
"title": "The continuum limit of sl(N/K) integrable super spin chains",
"url": "https://arxiv.org/abs/solv-int/9905007"
},
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