Picture-Changing Operators and Space-Time Supersymmetry

We explore geometrical properties of fermionic vertex operators for a NSR superstring in order to establish connection between worldsheet and target space supersymmetries.The mechanism of picture-changing is obtained as a result of imposing certain constraints on a world-sheet gauge group of the NSR Superstring Theory. We find that picture-changing operators of different integer ghost numbers form a polynomial ring.By using properties of the picture-changing formalism, we establish a relation between the NSR and GS String theories.We show that, up to picture-changing transformations,the stress-energy tensor of the N = 1 NSR superstring theory can be obtained from the stress-energy tensor of the N = 1 GS superstring theory in a flat background by a simple field redefinition. The equations of motion of a GS superstring are shown to be fulfilled in the NSR operator formalism;they are also shown to be invariant under κ-symmetry,in terms of operator products in the NSR theory. This allows us to derive the space-time supersymmetry transformation laws for the NSR String Theory. Then,we explore the properties of the κ-symmetry in the NSR formalism and find that it leads to some new relations between bosonic and fermionic correlation functions. December 94 † [email protected]