Abstract
We study several aspects of the N=1 super Liouville theory. We show that certain elements of the fusion matrix in the Neveu–Schwarz sector are related to the structure constants according to the same rules which we observe in rational conformal field theory. We collect some evidences that these relations should hold also in the Ramond sector. Using them the Cardy–Lewellen equation for defects is studied, and defects are constructed.
Highlights
During the last decades we got deep understanding of the properties of rational conformal field theories having a finite number of primaries
We study several aspects of the N = 1 super Liouville theory
We show that certain elements of the fusion matrix in the Neveu-Schwarz sector related to the structure constants according to the same rules which we observe in rational conformal field theory
Summary
During the last decades we got deep understanding of the properties of rational conformal field theories having a finite number of primaries. We have formulas for boundary states [5], and defects [6,7] in rational conformal field theories. In this paper we study the following relations, proved in rational CFT without multiplicities (fusion numbers Njik = 0, 1), in N = 1 super Liouville field theory: F0,i jk j k∗. The second relation (3) results from the bootstrap equation combined with the pentagon identity [5, 26,27,28] These relations were examined in the Lioville field theory. In [28] (3) and (4) in the Liouville field theory were checked using the relation of the fusion matrix with boundary three-point function. We find that for N = 1 super Liouville theory the susy version of this formula leads to the corresponding generalization of the relations (3) and (4). SR(Q + τ − α1)SR(τ + α4 SNS(Q + τ + α4 − αt)SNS(τ α3)SR(τ + α1)SR(τ αt)SNS(Q + τ + α2
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
