Integrability of the boundary sine-Gordon model

Abstract

We construct a boundary Lagrangian for the N = 2 supersymmetric sine-Gordon model which preserves (B-type) supersymmetry and integrability to all orders in the bulk coupling constant g. The supersymmetry constraint is expressed in terms of matrix factorisations. * mattik@phys.ethz.ch

The RR charges of the A-type Gepner models

“…This list of models agrees with that of table 1, except for the model P (1,6,21,28,28) [84], for which the matrix factorisation analysis predicts that a generalised permutation factori-sation is required in the factor ( 23), while the conformal field theory analysis predicts that all RR charges can be accounted for in terms of the usual tensor product and permutation branes. This mismatch is easily resolved: the generalised permutation factorisation ( 23) is of the form…”

“…The matrix factorisation description of supersymmetric D-branes also applies to more general classes of Landau-Ginzburg models -see for example[28] for a recent discussion in the context of the N=2 sine-Gordon model.…”

Boundary fermions and the plane wave

“…The first nontrivial higher spin currents for this theory were formulated in [42,4]. In the language of a Landau-Ginzburg model with superpotential W = −2ig cos z + const (181) they can be found in [15]. Reintroducing the standard parameter ω and rescaling the coupling constant to g → − m ω 2 , the plane wave like theory with superpotential W = imz 2 is obtained from (181) in the ω → 0 limit.…”

“…The choice of a trigonometric superpotential W (z) ∼ cos z in the solutions of [11] leads to the integrable N = 2 supersymmetric sine-Gordon model on the worldsheet, whereas the exponential W (z) ∼ e z gives rise to the N = 2 Liouville theory. In the context of boundary fermions these theories have been discussed in [4,14,15] and [16].…”

“…From (65) and (66) in section 5 we have three real parameters as obtained to first order in the bulk coupling constant for the N = 2 sine-Gordon model in [4]. For the sine-Gordon model a calculation taking into account all order contributions reduces this number to a single boundary parameter as shown in [15]. In the case of present interest, however, contributions leading to these additional constraints vanish in the ω → 0 limit, compare especially with the quadratic form of (66) in comparison with the trigonometric boundary potential in [4,15] and the discussion in section 4.3 of [15].…”