Four-point Function in Super Liouville Gravity
Résumé
We consider the 2D super Liouville gravity coupled to the minimalsuperconformal theory. We analyze the physical states in the theory and givethe general form of the n-point correlation numbers on the sphere in terms ofintegrals over the moduli space. The three-point correlation numbers arepresented explicitly. For the four-point correlators, we show that the integralover the moduli space reduces to the boundary terms if one of the fields isdegenerate. It turns out that special logarithmic fields are relevant forevaluating these boundary terms. We discuss the construction of these fieldsand study their operator product expansions. This analysis allows evaluatingthe four-point correlation numbers. The derivation is analogous to the one inthe bosonic case and is based on the recently derived higher equations ofmotion of the super Liouville field theory.