2011
DOI: 10.1016/j.nuclphysb.2011.04.004
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Yangian superalgebras in conformal field theory

Abstract: Quantum Yangian symmetry in several sigma models with supergroup or supercoset as target is established. Starting with a two-dimensional conformal field theory that has current symmetry of a Lie superalgebra with vanishing Killing form we construct non-local charges and compute their properties. Yangian axioms are satisfied, except that the Serre relations only hold for a subsector of the space of fields. Yangian symmetry implies that correlation functions of fields in this sector satisfy Ward identities. We t… Show more

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Cited by 4 publications
(6 citation statements)
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References 92 publications
(114 reference statements)
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“…The only singular vector is then the highest weight state, so this quotient module is irreducible. 6 We denote it by A n+1/2,0 as its zero-grade subspace has N 0 -eigenvalue n + 1 2 . The character of this atypical irreducible is now obtained by imposing a 0 = 0 in Equation (3.10).…”
Section: Representation Theorymentioning
confidence: 99%
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“…The only singular vector is then the highest weight state, so this quotient module is irreducible. 6 We denote it by A n+1/2,0 as its zero-grade subspace has N 0 -eigenvalue n + 1 2 . The character of this atypical irreducible is now obtained by imposing a 0 = 0 in Equation (3.10).…”
Section: Representation Theorymentioning
confidence: 99%
“…They appear in many important problems in string theory and condensed matter physics, for example the AdS/CFT correspondence [1] and the theory of disordered systems [2,3]. Questions about these problems may often be related to WZW models and their cosets through appropriate perturbations [4][5][6][7].Over the last few years, there has been significant progress in the understanding of WZW models on supergroups. Correlation functions of WZW models on type I supergroups can be computed in principle [8].…”
mentioning
confidence: 99%
“…81 We thank E. Ragoucy for suggesting the idea and for discussions about this point. 82 We thank P. Sorba for a discussion about this point.…”
Section: Discussionmentioning
confidence: 99%
“…Inside such a closure, denominators of central elements, like those appearing in (62), can be given an abstract meaning. Unfortunately, it is very hard to equip such closures with a Hopf algebra structure in general 81 .…”
Section: Discussionmentioning
confidence: 99%
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