In this paper, exact one-point functions of N = 1 super-Liouville field theory in two-dimensional space-time with appropriate boundary conditions are presented. Exact results are derived both for the theory defined on a pseudosphere with discrete (NS) boundary conditions and for the theory with explicit boundary actions which preserves super conformal symmetries. We provide various consistency checks. We also show that these one-point functions can be related to a generalized Cardy conditions along with corresponding modular S-matrices. Using this result, we conjecture the dependence of the boundary two-point functions of the (NS) boundary operators on the boundary parameter.

Fusion rules, structure constants and 4-point functions for all the fields in the Neveu-Schwarz, Ramond and twisted sectors of N = 2 minimal models are presented. It is shown that the additional Zp+2 symmetries of these models are generated by specific chiral N = 2 superfields. The structure of the corresponding N = 2 superparafermionic models is discussed.

In this letter we propose exact three-point correlation functions for N = 1 supersymmetric Liouville theory. Along the lines of [12] we propose a generalized special function which describe the three-point amplitudes. We consider briefly the so called reflection amplitudes in the supersymmetric case. 1

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We derive one-point functions of the N = 2 super-Liouville theory on a half line using the modular transformations of the characters in terms of the bulk and boundary cosmological constants. We also show that these results are consistent with conformal bootstrap equations which are based on the bulk and boundary actions. We provide various independent checks for our results. 1 ahn@ewha.ac.kr