Conformal invariance and quantum integrability of sigma models on symmetric superspaces

Abstract

We consider two dimensional non linear sigma models on few symmetric superspaces, which are supergroup manifolds of coset type. For those spaces where one loop beta function vanishes, two loop beta function is calculated and is shown to be zero. Vanishing of beta function in all orders of perturbation theory is shown for the principal chiral models on group supermanifolds with zero Killing form. Sigma models on symmetric (super) spaces on supergroup manifold G/H are known to be classically integrable. We investigate a possibility to extend an argument of absence of quantum anomalies in non local current conservation from non super case to the case of supergroup manifolds which are asymptotically free in one

Free fermion resolution of supergroup WZNW models

“…constitute the isometries of superspheres S 2n+m−1|2n [5,89]. Moreover, these series include the special cases D(2, 1; α) and D(n + 1, n) which have been shown [22] to have similarly exciting properties as A(n, n) = psl(n + 1|n + 1) [23]. Let us note that the WZNW models based on the family of exceptional Lie superalgebras D(2, 1; α) are also relevant for a manifestly supersymmetric description of string backgrounds involving AdS 3 × S 3 × S 3 .…”

“…for non-compact groups, they should also be included in the definition of the labels µ. 22 It is the dual which is relevant here since we assume the antiholomorphic current superalgebra to mimic the differential operators (4.4), not those in (4.3). Notice that the roles of S a 1 and S2a are exchanged in these expressions.…”

“…Let us denote the image of the field (5.19) underΞ by Φ a µ;b . According to our general strategy, correlation functions in the interacting theory may be computed through 22) where the correlators on the right hand side are to be evaluated in the decoupled theory. We shall show below that correlators with s ≥ s max = N r insertions vanish so that the summation over s is finite.…”

“…The same class of supergroup σ-models is also known to admit a new kind of marginal deformations that are not of current-current type [23,24]. Finally, there seems to be a striking correspondence between the integrability of these models and their conformal invariance [25,26,21,22].…”

Multi-parametric R-matrix for the $\mathfrak {sl}(2|1)$sl(2|1) Yangian

“…Later on, sigma models on a variety of supergroup manifolds, and their Gross-Neveu like analogs, were successfully investigated by integrability methods. Especially interesting is the relation of integrable structures to the CFT ones, when the sigma model is not only integrable but also conformal with a non chiral conformal symmetry [8,13].…”