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 then show that this symmetry is preserved by certain perturbations of the conformal field theory. The main example are sigma models of the supergroups PSL(N|N), OSP(2N+2|2N) and D(2,1;α) away from the WZW point. Further there are the OSP(2N+2|2N) Gross-Neveu models and current-current perturbations of ghost systems, both for the disc as world-sheet. The latter we show to be equivalent to CP N−1|N sigma models, while the former are conjecturally dual to supersphere sigma models. *

Relating the archetypes of logarithmic conformal field theory

“…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).…”

“…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].…”

Yangians,S-matrices and AdS/CFT

“…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.…”

“…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 .…”

“…13 The reader is referred to the standard literature (see for example [72][73][74]) for a treatment of this subject. For the generalization to simple Lie superalgebras, see for instance [75][76][77][78][79][80][81]. 14 In the AdS/CFT case, attempts to formulate the Yangian in this fashion meet some obstacles.…”