Higher equations of motion in the N = 1 SUSY Liouville field theory

As in the ordinary bosonic Liouville field theory, in its N = 1 supersymmetric version, an infinite set of operator valued relations, the "higher equations of motions," hold. The equations are in one to one correspondence with the singular representations of the super Virasoro algebra and enumerated by a pair of natural numbers (m, n). We explicitly demonstrate these equations in the classical case, where the equations of type (1, n) survive and can be interpreted directly as relations for classical fields. The general form of higher equations of motion is established in the quantum case, both for the Neveu-Schwarz and Ramond series.