Michihiro Naka

Singular Calabi-Yau manifolds and ADE classification of CFTS

Abstract 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 of A 2 ⊗A 2 ,A 2 ⊗A 3 ,A 2 ⊗A 4 should 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.

Boundary state description of tachyon condensation

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 (Frau et al. hep-th/9903123). In this description we show how the RR-charge of the lower-dimensional D-branes emerges. We also investigate the tachyon condensation in 4/2 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.

Critical level statistics of the Fibonacci model

We numerically analyze spectral properties of the Fibonacci model which is a one-dimensional quasiperiodic system. We find that the energy levels of this model have the distribution of the band widths

Geometric engineering of Seiberg-Witten theories with massive hypermultiplets

w

Landau–Ginzburg description of D-branes on ALE spaces

obeys

A Realization of N=1

P_B(w)\sim w^{\alpha}

Algebras with Wolf Spaces

(w\to 0)

Remarks on N = 1 (3/2,2) algebras

and

Coset construction of metrics with special holonomy

P_B(w) \sim e^{-\beta w}