We extend the construction of the boundary states in Gepner models to the nondiagonal modular invariant theories, and derive the same supersymmetric conditions as the diagonal theories. We also investigate the relation between the microscopic charges of the boundary states and Ramond charges of the B-type D-branes on the Calabi-Yau threefolds with one Kähler modulus in the large volume limit. *
We study Ricci-flat metrics on non-compact manifolds with the exceptional holonomy Spin(7), G2. We concentrate on the metrics which are defined on R × G/H. If the homogeneous coset spaces G/H have weak G2, SU(3) holonomy, the manifold R × G/H may have Spin(7), G2 holonomy metrics. Using the formulation with vector fields, we investigate the metrics with Spin(7) holonomy on R × Sp(2)/Sp(1), R × SU(3)/U(1). We have found the explicit volume-preserving vector fields on these manifolds using the elementary coordinate parametrization. This construction is essentially dual for solving the generalized self-duality condition for spin connections. We present the most general differential equations for each coset. Then, we develop a similar formulation in order to calculate metrics with G2 holonomy.
We construct the explicit boundary state description of the vortex-type (codimension two) tachyon condensation in brane-antibrane systems generalizing the known result of the kink-type . In this description we show how the RR-charge of the lower dimensional D-branes emerges. We also investigate the tachyon condensation in T 4 /Z 2 orbifold and find that the twisted sector can be treated almost in the same way as the untwisted sector from the viewpoint of the boundary state. Further we discuss the higher codimension cases.
We study superstring propagations on the Calabi-Yau manifold which develops an isolated ADE singularity. This theory has been conjectured to have a holographic dual description in terms of N = 2 Landau-Ginzburg theory and Liouville theory. If the Landau-Ginzburg description precisely reflects the information of ADE singularity, the Landau-Ginzburg model of D 4 , E 6 , E 8 and Gepner model ofshould give the same result. We compute the elements of D 4 , E 6 , E 8 modular invariants for the singular Calabi-Yau compactification in terms of the spectral flow invariant orbits of the tensor product theories with the theta function which encodes the momentum mode of the Liouville theory. Furthermore we find the interesting identity among characters in minimal models at different levels. We give the complete proof for the identity. *
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