Relative (pre)-modular categories from special linear Lie superalgebras

Abstract We examine two different m-traces in the category of representations over the quantum Lie superalgebra associated to sl ( m | n ) at root of unity. The first m-trace is on the ideal of projective modules and leads to new Extended Topological Quantum Field Theories. The second m-trace is on the ideal of perturbative typical modules. We consider the quotient with respect to negligible morphisms coming from this m-trace and show that in the case of sl ( 2 | 1 ) this quotient leads to 3-manifolds invariants. We conjecture that the quotient category of perturbatives over quantum sl ( m | n ) leads to 3-manifold invariants and more generally ETQFTs.