arXiv subjects

Michihiro Naka

Publications and source records attributed to Michihiro Naka.

8 recordsLinked to original sources

arXiv2004

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 $w$ obeys $P_B(w)\sim w^α$ $(w\to 0)$ and $P_B(w) \sim e^{-βw}$ $(w\to\infty)$, the gap distribution $P_G(s)\sim s^{-δ}$ $(s\to 0)$ ($α,β,δ>0$) . We also compare the results with those of multi-scale Cantor sets. We find qualitative differences between the spectra of the Fibonacci model and the multi-scale Cantor sets.

cond-mat.stat-mech↗

arXiv2003

Geometric Engineering of Seiberg-Witten Theories with Massive Hypermultiplets

We analyze the geometric engineering of the N=2 SU(2) gauge theories with $1\leq N_f\leq 3$ massive hypermultiplets in the vector representation. The set of partial differential equations satisfied by the periods of the Seiberg-Witten differential is obtained from the Picard-Fuchs equations of the local B-model. The differential equations and its solutions are consistent with the massless case. We show that the Yukawa coupling of the local A-model gives rise to the correct instanton expansion in the gauge theory, and propose the pattern of the distribution of the world-sheet instanton number from it. As a side result, we obtain the asymptotic form of the instanton number in the gauge theories with massless hypermultiplets.

hep-th↗

arXiv2003

A Realization of N=1 ${\cal SW}(3/2,2)$ Algebras with Wolf Spaces

We find out that some unitary minimal models of the N=1 ${\cal SW}(3/2,2)$ superconformal algebra can be realized as the level one coset models based on the Wolf spaces $SU(n)/(SU(n-2)\times SU(2))$. We obtain the expression of the fermionic current with the conformal weight 5/2 in the algebra. Then, these models are twisted to give the topological conformal field theories.

hep-th↗

arXiv2002

Various Wrapped Branes from Gauged Supergravities

We study wrapped brane configurations via possible maximally supersymmetric gauged supergravities. First, we construct various supersymmetric wrapped D3 brane configurations from D=5 N=8 SO(6) gauged supergravity. This procedure provides certain new examples of wrapped D3 branes around supersymmetric cycles inside non-compact special holonomy manifolds. We analyze their behaviors numerically in order to discuss a correspondence to Higgs and Coulomb branches of sigma models on wrapped D3 branes. We also realize supersymmetric wrapped M2 branes from D=4 N=8 SO(8) gauged supergravity. Then, we study supersymmetric wrapped type IIB NS5 branes by D=7 N=4 SO(4) gauged supergravity. We show a method to derive them by using supersymmetric wrapped M5 branes in D=7 N=4 SO(5) gauged supergravity. This method is based on a domain wall like reduction. Solutions include NS5 branes wrapped around holomorphic $CP^2$ inside non-compact Calabi-Yau threefold. Their behavior shows a similar feature to that for NS5 branes wrapped around holomorphic $CP^1$ inside non-compact $K3$ surface. This construction also provides a check of preserved supersymmetry for a solution interpreted within a string world-sheet theory introduced by Hori and Kapustin. Finally, we find new non-supersymmetric solutions including AdS space-times in D=6 N=2 $SU(2)\times U(1)$ massive gauged supergravity. These solutions can be interpreted as non-supersymmetric wrapped D4-D8 configurations which are dual to non-supersymmetric conformal field theories realized on wrapped D4 branes.

hep-th↗

arXiv2000

Landau-Ginzburg Description of D-branes on ALE Spaces

We study the Landau-Ginzburg (LG) mirror theory of the non-linear sigma model on the ALE space ${\cal M}$ obtained by resolving the singularity of the orbifold ${\bf C}^2/{\bf Z}_N$. In the LG description, the data of the BPS spectrum and the lines of marginal stability are encoded in the special Lagrangian submanifolds of the mirror manifold $\hat{\cal M}$. Our LG description is quite simple as compared with the quiver gauge theory analysis near the orbifold point. Furthermore our mirror analysis can be applied to any point on the moduli space of ${\cal M}$.

hep-th↗

arXiv2000

Singular Calabi-Yau Manifolds and ADE Classification of CFTs

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 $A_2\otimes A_2, A_2\otimes A_3, A_2\otimes A_4$ 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.

hep-th↗

arXiv2000

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 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.

hep-th↗

arXiv2000

Boundary states in Gepner models

We extend the construction of the boundary states in Gepner models to the non-diagonal 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.

hep-th↗