Conformal invariance and quantum integrability of sigma models on symmetric superspaces

TL;DR

This paper investigates the quantum properties and integrability of two-dimensional sigma models on symmetric superspaces, demonstrating vanishing beta functions at multiple loops and exploring quantum anomaly absence in supergroup contexts.

Contribution

It extends the understanding of quantum integrability and beta function behavior to sigma models on supergroup manifolds, including proofs of all-order vanishing of the beta function for certain models.

Findings

Two-loop beta function vanishes for models with zero one-loop beta function.

Beta function vanishes to all orders in perturbation theory for principal chiral models on supergroups with zero Killing form.

Classical integrability extends to quantum level in specific supergroup sigma models.

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 loop.