Higher Equations of Motion in N = 1 SUSY Liouville Field Theory

TL;DR

This paper explores the higher equations of motion in N=1 supersymmetric Liouville field theory, establishing their classical and quantum forms and linking them to singular representations of the super Virasoro algebra.

Contribution

It explicitly demonstrates the higher equations of motion in the classical case and generalizes their form to the quantum case for both Neveu-Schwarz and Ramond series.

Findings

Classical higher equations of motion are explicitly demonstrated.

Quantum form of the higher equations of motion is established.

Equations correspond to singular representations of the super Virasoro algebra.

Abstract

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