arXiv subjects

Tomomi Muto

Publications and source records attributed to Tomomi Muto.

9 recordsLinked to original sources

arXiv2005

A relation between moduli space of D-branes on orbifolds and Ising model

We study D-branes transverse to an abelian orbifold C^3/Z_n Z_n. The moduli space of the gauge theory on the D-branes is analyzed by combinatorial calculation based on toric geometry. It is shown that the calculation is related to a problemto count the number of ground states of an antiferromagnetic Ising model. The lattice on which the Ising model is defined is a triangular one defined on the McKay quiver of the orbifold.

hep-th↗

arXiv2002

D-geometric Structure of Orbifolds

We study D-branes on abelian orbifolds C^d/Z_N for d=2, 3. The toric data describing the D-brane vacuum moduli space, which represents the geometry probed by D-branes, has certain redundancy compared with the classical geometric description of the orbifolds. We show that the redundancy has a simple combinatorial structure and find analytic expressions for degrees of the redundancy. For d=2 the structure of the redundancy has a connection with representations of SU(N) Lie algebra, which provides a new correspondence between geometry and representation theory. We also prove that non-geometric phases do not appear in the Kahler moduli space for d=2.

hep-th↗

arXiv2001

Stability of Quiver Representations and Topology Change

We study phase structure of the moduli space of a D0-brane on the orbifold C^3/Z_2 \times Z_2 based on stability of quiver representations. It is known from an analysis using toric geometry that this model has multiple phases connected by flop transitions. By comparing the results of the two methods, we obtain a correspondence between quiver representations and geometry of toric resolutions of the orbifold. It is shown that a redundancy of coordinates arising in the toric description of the D-brane moduli space, which is a key ingredient of disappearance of non-geometric phases, is understood from the monodromy around the orbifold point. We also discuss why only geometric phases appear from the viewpoint of stability of D0-branes.

hep-th↗

arXiv1999

Brane Cube Realization of Three-dimensional Nonabelian Orbifolds

We study D-branes on three-dimensional orbifolds ${\bf C}^3/Γ$ where $Γ$ are finite subgroups of SU(3). The quiver diagram of $\ZnZn \in SU(3)$ can be expressed in three-dimensional form. According to the correspondence between quiver diagrams and brane configurations, we construct a brane configuration for ${\bf C}^3/\ZnZn$ which has essentially three-dimensional structrue. Brane configurations for nonabelian orbifolds $\C^3/Δ(3n^2)$ and $\C^3/Δ(6n^2)$ are obtained from that for $\C^3/\ZnZn$ by certain quotienting procedure.

hep-th↗

arXiv1999

Brane Configurations for Three-dimensional Nonabelian Orbifolds

We study brane configurations corresponding to D-branes on complex three-dimensional orbifolds ${\bf C}^3/Γ$ with $Γ=Δ(3n^2)$ and $Δ(6n^2)$, nonabelian finite subgroups of SU(3). We first construct a brane configuration for ${\bf C}^3/{\bf Z}_n \times {\bf Z}_n$ by using D3-branes and a web of (p,q) 5-branes of type IIB string theory. Brane configurations for the nonabelian orbifolds are obtained by performing certain quotients on the configuration for ${\bf C}^3/{\bf Z}_n \times {\bf Z}_n$. Structure of the quiver diagrams of the groups $Δ(3n^2)$ and $Δ(6n^2)$ can be reproduced from the brane configurations. We point out that the brane configuration for ${\bf C}^3/Γ$ can be regarded as a physical realization of the quiver diagram of $Γ$. Based on this observation, we discuss that three-dimensional McKay correspondence may be interpreted as T-duality.

hep-th↗

arXiv1999

D-branes on Three-dimensional Nonabelian Orbifolds

We study D-branes on a three complex dimensional nonabelian orbifold ${\bf C}^3/Γ$ with $Γ$ a finite subgroup of SU(3). We present general formulae necessary to obtain quiver diagrams which represent the gauge group and the spectrum of the D-brane worldvolume theory for dihedral-like subgroups $Δ(3n^2)$ and $Δ(6n^2)$. It is found that the quiver diagrams have a similar structure to webs of branes.

hep-th↗

arXiv1997

D-branes on Orbifolds and Topology Change

We consider D-branes on an orbifold $C^3/Z_n$ and investigate the moduli space of the D-brane world-volume gauge theory by using toric geometry and gauged linear sigma models. For $n=11$, we find that there are five phases, which are topologically distinct and connected by flops to each other. We also verify that non-geometric phases are projected out for $n=7,9,11$ cases as expected. Resolutions of non-isolated singularities are also investigated.

hep-th↗

arXiv1996

On thermodynamics of black p-branes

Thermodynamic properties of a class of black $p$-branes in $D$-dimensions considered by Duff and Lu are investigated semi-classically. For black $(d-1)$-brane, thermodynamic quantities depend on $D$ and $d$ only through the combination $\tilde d \equiv D-d-2$. The behavior of the Hawking temperature and the lifetime vary with $\tilde d$, with a critical value $\tilde d=2$. For $\tilde d>2$, there remains a remnant, in which non-zero entropy is stored. Implications of the fact that the Bekenstein-Hawking entropy of the black $(d-1)$-brane depend only on $\tilde d=D-d-2$ is discussed from the point of view of duality.

hep-th↗

arXiv1994

Axial-Vector Duality as a Mirror Symmetry

We study $N=2$ supersymmetric $SU(2)/U(1)$ and $SL(2,R)/U(1)$ gauged Wess-Zumino-Witten models. It is shown that the vector gauged model is transformed to the axial gauged model by a mirror transformation. Therefore the vector gauged model and the axial gauged model are equivalent as $N=(2,2)$ superconformal field theories. In the $SL(2,R)/U(1)$ model, it is known that axial-vector duality relates a background with a singularity to that without a singularity. Implications of the equivalence of these two models to space-time singularities are discussed.

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