Supersymmetric, Integrable Toda Field Theories: The B(1,1) Model

TL;DR

This paper explores the supersymmetric Toda field theory based on the B(1,1) superalgebra, constructing quantum W-currents, analyzing fermionic affinization, and demonstrating the model's integrability and renormalization properties.

Contribution

It introduces the quantum W-currents for the B(1,1) supersymmetric Toda theory and proves the conservation of higher-spin currents to all orders.

Findings

The B(1,1) model has a real, non-renormalized particle mass spectrum.

Construction of the first higher-spin conserved current and proof of its all-loop conservation.

Consistency between charge and mass renormalization is verified.

Abstract

We study the two-dimensional supersymmetric Toda theory based on the Lie superalgebra $B(1,1) \equiv Osp(3|2)$ and construct its quantum W-currents. We also investigate the fermionic affinization of this model: we show that despite the non-unitary form of the Lagrangian the $B^{(1)}(1,1)$ theory has a real particle mass spectrum which is not renormalized at one-loop. We construct the first higher--spin conserved current, prove its conservation to all-loop order, compute one-loop corrections to the corresponding charge and check consistency between charge and mass renormalization.