Quantum invariants arising from $U_h\mathfrak{s}\mathfrak{l}(2\mathrm{\mid }1)$ are q-holonomic

We show that the quantum invariants arising from typical representations of the quantum group $U_h\mathfrak{s}\mathfrak{l}(2\mathrm{\mid }1)$ are q-holonomic. In particular, this implies the existence of an underlying field theory for which this family of invariants are partition functions.