D-branes at multicritical points

Abstract

The moduli space of c = 1 conformal field theories in two dimensions has a multicritical point, where a circle theory is equivalent to an orbifold theory. We analyse all the conformal branes in both descriptions of this theory, and find convincing evidence that the full brane spectrum coincides. This shows that the equivalence of the two descriptions at this multicritical point extends to the boundary sector. We also perform the analogous analysis for one of the multicritical points of the N = 1 superconformal field theories at c = 3 2 . Again the brane spectra are identical for both descriptions, however the identification is more subtle. *

Bulk-induced boundary perturbations for {\cal N}=1 superconformal field theories on the circle

“…In this paper we study the N = 1 supersymmetric analogue of this problem. The moduli space of N = 1 superconformal branes for the free boson and fermion theory has a similar structure as in the bosonic case [4,7], and there is also a close relation to the SU(2) WZW model, this time at k = 2 [8,9]. 1 However, there are also some differences: the WZW model description only applies to the superaffine theory at R = 1 (not one of the circle theories), and one needs to keep track carefully of the GSO-projection.…”

“…We shall first analyse the situation for the superaffine theory (which is equivalent to the WZW model at level 2), and then deduce from this the results for the circle theory at radius R = 1 by considering the circle theory as the Z 2 orbifold of the superaffine theory. In order to translate between the different descriptions, we first need to understand the dictionary between the brane descriptions in the different setups in some detail; some aspects of this were already analysed in [9].…”

“…We first review the description of the superaffine branes from [9]. We are interested in the branes ||B that preserve the superconformal (but not necessarily any larger) symmetry.…”

“…where G (andḠ) denotes the supercurrent of the N = 1 superconformal algebra -we use the same conventions as in [4] -and η = ± labels the two possible choices for the N = 1 gluing conditions. As explained in [9], the Ishibashi states of the superaffine theory at R = 1 are labelled by the usual triplets (j; m, n), together with the sign η = ±. In the NS-NS sector all combinations with j integer appear, while j is half-integer in the R-R sector.…”

ℤ2 boundary twist fields and the moduli space of D-branes

“…It turns out that the two branches in the picture intersect, since the orbifold theory at R = √ 2 is equivalent to the circle theory at R = 2 √ 2, which corresponds to the continuum limit of the XY-model at the Kosterlitz-Thouless point [22]. This duality is valid also at the level of boundary CFT; it has been shown that the two bulk CFT admit the same boundary conditions and boundary operators or, in string theory language, the same set of D-branes [23]. This leads us to the idea of bosonizing boundary changing operators (the bosonized twist fields) in terms of another boson compactified on S 1 .…”