Critical Composite Superconformal String

Abstract

In the paper the nilpotent conditions of BRST operator for new superconformal string model were found. This string includes anticommutation $2-d$ fields additional to the standard Neveu-Schwarz superconformal set which carry quark quantum numbers. In this case the superconformal symmetry is realized by a non-linear way. In the superconformal composite string new constraints for 1 and 1/2 conformal dimension should be added to the standard system of Virasoro superalgebra constraints for 2 and 3/2 conformal dimensions. The number $N$ of the constraints and numbers $D$ and $D'$ of bosonic and fermionic $2-d$ fields are connected by a simple relationship $D'/2+D-3N-15=0.$ Also perspectives of the critical composite superconformal string are discussed.