Theory of Superdualities and the Orthosymplectic Supergroup

TL;DR

This paper develops a theoretical framework for dualities in sigma models involving both fermions and bosons, introducing the orthosymplectic supergroup as a unifying duality group and extending existing duality analyses.

Contribution

It generalizes duality groups to the orthosymplectic supergroup OSp(m,m|2n) and derives the most general D=2 sigma model with fermionic and bosonic couplings, extending Gaillard-Zumino analysis.

Findings

Orthosymplectic duality OSp(m,m|2n) unifies fermionic and bosonic dualities.

Derived the most general D=2 sigma model with such dualities.

Connected fermionic dualities to the orthosymplectic framework.

Abstract

We study the dualities for sigma models with fermions and bosons. We found that the generalization of the SO(m,m) duality for D=2 sigma models and the Sp(2n) duality for D=4 sigma models is the orthosymplectic duality OSp(m,m|2 n). We study the implications of this and we derive the most general D=2 sigma model, coupled to fermionic and bosonic one-forms, with such dualities. To achieve this we generalize Gaillard-Zumino analysis to orthosymplectic dualities, which requires to define embedding of the superisometry group of the target space into the duality group. We finally discuss the recently proposed fermionic dualities as a by-product of our construction.