Motoi Tachibana

Many-Brane Extension of the Randall-Sundrum Solution

Recently, Randall and Sundrum proposed a static solution to the Einstein equations in 5 spacetime dimensions with two 3-branes located at the fixed points of S 1 /Z2 to solve the hierarchy problem. We extend the solution and construct static and also inflationary solutions to the Einstein equations in 5 spacetime dimensions, one of which is compactified on S 1 , with any number of 3-branes whose locations are taken to be arbitrary. We discuss how the hierarchy problem can be explained in our model. 1. Introduction Recently, Randall and Sundrum 1) proposed a new interesting mechanism with a single small extra dimension for solving the hierarchy problem between the Planck scale and the weak scale. A key ingredient ofthis mechanism is that the metric is not factorizable and that the 4-dimensional metric is multiplied by a warp factor which is a rapidly changing function of the extra dimension. They explicitly constructed such a solution to the Einstein equations in 5 spacetime dimensions, one ofwhich is compactified on S 1 /Z2, with two 3-branes located at the fixed points of S 1 /Z2. For a solution to exist, it is crucial to take into account the effect ofthe branes on the bulk gravitational metric. In the Randall-Sundrum model, the number of3-branes is 2 and the locations are taken to be the fixed points of S 1 /Z2. Although this setup is motivated by recent developments in string and M-theory, 2) it would be ofinterest to construct new solutions to the 5-dimensional Einstein equations with many 3-branes. In this paper, we explicitly construct solutions with an arbitrary number of3-branes which are put at arbitrary positions in the direction ofthe extra dimension. Our motivation f this is threefold. First, it is known that any number of parallel D-branes can be put at arbitrary positions and that the gauge dynamics depend on the distances ofmultiple D-branes. Thus, it is physically meaningful to construct solutions corresponding to many 3-branes put at arbitrary positions. Second, many-brane configurations could explain other hierarchy problems, such as the fermion mass hierarchy. The origi

Spontaneously broken translational invariance of compactified space

Abstract We propose a mechanism to break the translational invariance of compactified space spontaneously. As a simple model, we study a real φ 4 model compactified on M D −1 ⊗ S 1 in detail, where we impose a nontrivial boundary condition on φ for the S 1 -direction. It is shown that the translational invariance for the S 1 -direction is spontaneously broken when the radius R of S 1 becomes larger than a critical radius R ∗ and also that the model behaves like a φ 4 model on a single kink background for R →∞. It is pointed out that spontaneous breakdown of translational invariance is accompanied by that of some global symmetries, in general, in our mechanism.

Dilaton coupled brane-world and field trapping

We address solutions of a brane-world with a cosmological constant

A New Mechanism of Spontaneous SUSY Breaking

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Holographic cold nuclear matter as dilute instanton gas

by introducing the dilaton in 5D bulk, and we examine the localization of the graviton, gauge bosons, and dilaton. For those solutions, we find that both the graviton and gauge bosons can be trapped for either sign, positive or negative, and a wide range of

Holographic cold nuclear matter and neutron star

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Classical aspects of the abelian Higgs model on the light front

due to the nontrivial dilaton, while the dilaton cannot be trapped on the brane.

Tunneling in Quantum Cosmology and Holographic SYM theory

We propose a new mechanism of spontaneous supersymmetry breaking. The existence of extra dimensions with nontrivial topology plays an important role. We investigate new features resulting from this mechanism in two simple supersymmetric Z2 and U (1) models. One noteworthy feature is that there exists a phase in which the translational invariance for the compactified directions is broken spontaneously, accompanying the breakdown of supersymmetry. The mass spectrum of the models appearing in reduced dimensions is full of variety, reflecting the highly nontrivial vacuum structure of the models. Nambu-Goldstone bosons (fermions) associatedwith the breakd own of symmetries are foundin the mass spectrum. The mechanism we propose also yields quite different vacuum structures for models with different global symmetries.

Duality and superconvergence relation in supersymmetric gauge theories

We study cold nuclear matter based on the holographic gauge theory, where baryons are introduced as the instantons in the probe D8/D8 branes according to the Sakai-Sugimoto model. Within a dilute gas approximation of instantons, we search for the stable states via the variational method and fix the instanton size. We find the first order phase transition from the vacuum to the nuclear matter phase as we increase the chemical potential. At the critical chemical potential, we could see a jump in the baryon density from zero to a finite definite value. While the size of the baryon in the nuclear matter is rather small compared to the nucleus near the transition point, where the charge density is also small, it increases with the baryon density. Those behaviors obtained here are discussed by relating them to the force between baryons.

Quantum Mechanics of Dynamical Zero Mode in

We have previously found a new phase of cold nuclear matter based on a holographic gauge theory, where baryons are introduced as instanton gas in the probe branes. In our model, we could obtain the equation of state (EOS) of our nuclear matter by introducing Fermi momentum. Then, here we apply this model to the neutron star and study its mass and radius by solving the Tolman–Oppenheimer–Volkoff (TOV) equations in terms of the EOS given here. We give some comments for our holographic model from a viewpoint of the other field theoretical approaches.