On the two dimensional gravity and W gravity

Abstract

Two dimensional quantum supergravity is analyzed. We find that the N=1 supergavity has a hidden OSP(1/2) current symmetry which make to solve the theory completely, being consistent with the space time dimension $d\le{1},\;d\ge{9}$. The N=2 supergravity has also OSP(2/2) symmetry and realistic for any dimension. This stems from the fact that the dimensionality (number of bosonic generators - number of fermionic generators) is zero.