Boundary states in c=−2 logarithmic conformal field theory

Abstract

Starting from first principles, a constructive method is presented to obtain boundary states in conformal field theory. It is demonstrated that this method is well suited to compute the boundary states of logarithmic conformal field theories. By studying the logarithmic conformal field theory with central charge c = −2 in detail, we show that our method leads to consistent results. In particular, it allows to define boundary states corresponding to both, indecomposable representations as well as their irreducible subrepresentations.

Nonsemisimple Fusion Algebras and the Verlinde Formula

“…For example, one can imagine that a boundary condition involves only an indecomposable representation, but not its subquotients (cf. [25,26]). A preliminary analysis shows that for p = 2, 3, invariants where in each case, the coefficients h 1,2 must be chosen such that the matrix entries are integers, for example, h 1 = h 2 = 2 for p = 3.…”

The logarithmic triplet theory with boundary

“…Little is known in general about the structure of a logarithmic boundary theory [37,38,39,40], and even for the simplest 'rational' theory, the triplet theory at c = −2, the situation is somewhat unclear. Various attempts to analyse the boundary conditions for this theory have been made in the past [38,39,40,16,41,42], but these are partially conflicting and no clear consensus seems to have emerged.…”

Minimal superstrings and loop gas models

“…This theory has been extensively studied [66,67,68,69,70,71,72,73] as the simplest example of a logarithmic CFT. There is a free field representation of the model in terms of a pair of Grassmann odd scalars Θ + (z,z) and Θ − (z,z).…”

“…Open string boundary conditions for symplectic fermions have been studied in [71,72,73]. Boundary states preserving the W -algebra are either Neumann or Dirichlet, where the plus (minus) signs correspond to Dirichlet (Neumann) boundary conditions.…”

“…Section 6 contains some concluding remarks. An appendix reviews properties of the c M = −2 "symplectic fermions" CFT [66,67,68,69,70,71,72,73], and details some of its uses in connection with minimal superstrings.…”