How to Superize Liouville Equation

Abstract

So far, there are described in the literature two ways to superize the Liouville equation: for a scalar field (for N ≤ 4) and for a vector-valued field (analogs of the Leznov – Saveliev equations) for N=1. Both superizations are performed with the help of Neveu–Schwarz superalgebra. We consider another version of these superLiouville equations based on the Ramond superalgebra, their explicit solutions are given by Ivanov–Krivonos’ scheme. Open problems are offered.