Loop Virasoro Lie conformal superalgebra

The loop Virasoro conformal superalgebra cls associated with the loop super-Virasoro algebra is constructed in the present paper. The conformal superderivation algebra of cls is completely determined, which is shown to consist of inner superderivations. And nontrivial free and free Z-graded cls-modules of rank two are classified. We also give a classification of irreducible free cls-modules of rank two and all irreducible submodules of each free Z-graded cls-module of rank two.