BOUNDARY STATES IN BOUNDARY LCFT: AN ALGEBRAIC APPROACH

It is well known that LCFT generally contains Jordan cell structure and, in our previous paper, we have proposed a conjecture that one and only one boundary sate is allowed in the rank-2 cell. With these states in c=-2 rational LCFT, we can express boundary states in the closed string picture, in regard to corresponding boundary conditions in the open string picture. In this paper, We briefly review our previous paper on boundary states in LCFTs. We also add one more proof which supports the conjecture, and confirm this doesn't change our previous results. This paper is based on the talk given at School & Workshop On Logarithmic Conformal Field Theory and Its Applications held in Tehran, Iran.