Worldsheet approaches to D-branes on supersymmetric cycles

Abstract

We consider D-branes wrapped around supersymmetric cycles of Calabi-Yau manifolds from the viewpoint of N=2 Landau-Ginzburg models with boundary as well as by consideration of boundary states in the corresponding Gepner models. The Landau-Ginzburg approach enables us to provide a target space interpretation for the boundary states. The boundary states are obtained by applying Cardy's procedure to combinations of characters in the Gepner models which are invariant under spectral flow. We are able to relate the two descriptions using the common discrete symmetries of the two descriptions. We are thus able to provide an extension to the boundary of the bulk correspondence between Landau-Ginzburg orbifolds and the corresponding Gepner models.Comment: 28 pages, LaTeX with revtex; (v2) Condition involving superpotential in the boundary LG model imposed, references included ; (v3) final version to appear in journa

D-branes in singular Calabi–Yau n-fold and N=2 Liouville theory

“…Technologies of describing D-branes using world-sheet theory have recently been developed considerably [19,20]. In particular the boundary state approach to D-branes in Gepner models has been discussed by various authors [21,22,23]. In this paper we will make a slight generalization of this construction to cope with the case of non-compact CFT consisting of Liouville field.…”

Matrix Factorizations, D-branes and their deformations

“…These fields fit into fermionic supermultiplets of the d = 1, N = 2 superalgebra, which can be compactly written as superfields of the form Π a ≡ (π a + θℓ a ), where ℓ a are auxiliary fields. A peculiarity of such superfields is that they are not truly chiral but satisfy [21,22] …”

D-branes on Calabi–Yau Manifolds and Superpotentials

“…The boundary conditions of interest to us are Dirichlet boundary conditions [19], which we take to be φ =φ = 0 and ψ + = ψ − ,ψ + =ψ − . It is useful to form the combinations…”