Shoichi Ichinose

Fermions in Kaluza-Klein and Randall-Sundrum theories

The Kaluza-Klein theory and Randall-Sundrum theory are examined comparatively, with focus on the behavior of the five dimensional (Dirac) fermion in the dimensional reduction to four dimensions. They are properly treated using the Cartan formalism. In the KK case, the dual property between the electric and magnetic dipole moments is revealed in relation to the ratio of two massive parameters: the inverse of the radius of the extra-space circle and the 5D fermion mass. The order estimation of the couplings is done. In the RS case, we consider the interaction with the 5D(bulk) Higgs field and the gauge field. The chiral property, localization, anomaly phenomena are examined. We evaluate the bulk quantum effect using the method of the induced effective action. The electric dipole moment term naturally appears. This is a new origin of the CP-violation. In the 4D limit, the dual relation between KK model and RS model appears. 1 This work is based on the content presented at the Fifth KEK Topical Conference

Casimir Energy of 5D Electromagnetism and New Regularization Based on Minimal-Area Principle

We examine the Casimir energy of 5D electromagnetism from the recent standpoint. The bulk geometry is flat. The Z2 symmetry and periodic property, for the extra coordinate, are taken into account. After confirming the consistency with the past result, we do new things based on a new regularization. In the treatment of the divergences, we introduce IR and UV cutoffs and restrict the (4D momentum, extra coordinate)-integral region. The regularized configuration is the sphere lattice, in the 4D continuum space, which changes along the extra coordinate. The change (renormalization flow) is specified by the minimal area principle; hence, this regularization configuration is stringlike. We do the analysis not in the Kaluza-Klein expanded form but in a closed form. We do not use any perturbation. The formalism is based on the heat-kernel approach using the position/momentum propagator. Interesting relations between the heat kernels and the P/M propagators are obtained, where we introduce the generalized P/M propagators. A useful expression of the Casimir energy, in terms of the P/M propagator, is obtained. The restricted region approach is replaced by the weight-function approach in the latter-half description. Its meaning, in relation to space-time quantization, is argued. Finite Casimir energy is numerically obtained. The compactification-size parameter (periodicity) suffers from the renormalization effect. Numerical evaluation is exploited. In particular, the minimal surface lines in the 5D flat space are obtained both numerically using the Runge-Kutta method and analytically using a general solution. Subject Index: 132, 133, 139

A solution of the Randall-Sundrum model and the mass hierarchy problem

A solution of the Randall-Sundrum model for a simplified case (one wall) is obtained. It is given by the 1/k2-expansion (thin-wall expansion), where 1/k is the thickness of the domain wall. The vacuum setting is done by the five-dimensional (5D) Higgs potential and the solution is for a family of the Higgs parameters. The mass hierarchy problem is examined. Some physical quantities in four-dimensional (4D) world such as the Planck mass, the cosmological constant and fermion masses are focused. Similarity to the domain wall regularization used in the chiral fermion problem is explained. We examine the possibility that the 4D massless chiral fermion bound to the domain wall in the 5D world can be regarded as real 4D fermions such as neutrinos, quarks and other leptons.

Weyl anomaly of 2D dilaton-scalar gravity and the Hermiticity of the system operator

Weyl Anomaly in the dilaton-scalar system in 2 dimensional gravity is examined. We take the heat-kernel regularization for the ultraviolet divergences. Generally the Weyl anomaly is determined by the 2nd order differential (elliptic) operator of the system and the definition of the measure. We have the freedom of the operator choice caused by the arbitrariness of total divergences (surface terms) in the action. We examine the Weyl anomaly in connection with such points and the hermiticity of the operator.

Wall and antiwall in the Randall-Sundrum model and a new infrared regularization

An approach to finding the field equation solution of the Randall-Sundrum model with the

Spontaneous symmetry breakdown in massless scalar electrodynamics and Brans-Dicke-type gravitational theory

{S}^{1}{/Z}_{2}

Some Properties of Domain Wall Solution in the Randall-Sundrum Model

extra axis is presented. We closely examine the infrared singularity. The vacuum is set by the five-dimensional Higgs boson field. Both the domain wall and the anti-domain-wall naturally appear, at the ends of the extra compact axis, by taking a new infrared regularization. The solution is considered to be stable by the kink boundary condition. A continuous (infrared-) regularized solution, which is a truncated Fourier series of a discontinuous solution, is utilized. The ultraviolet-infrared relation appears in the regularized solution.

BRS symmetry on background-field, Kallosh theorem and renormalization

Abstract The dynamical symmetry breaking through the Coleman-Weinberg phenomenon is examined in massless scalar electrodynamics and in a Brans-Dicke-type gravitational theory. The calculation of the effective potential is reformulated using the background-field method and dimensional regularization. Similarity between the two theories is stressed. For the case of the gravitational theory, a relation between the Higgs scalar mass and the gravitational constant is obtained. All one-loop counter-terms for the matterless Brans-Dicke theory are explicitly obtained and the problem of renormalizability is examined.

Casimir energy of the universe and new regularization of higher dimensional quantum field theories

Properties of the domain wall (kink) solution in the 5 dimensional RandallSundrum model are examined both analytically and numerically. The configuration is derived by the bulk Higgs mechanism. We focus on 1) the convergence property of the solution, 2) the stableness of the solution, 3) the non-singular property of the Riemann curvature, 4) the behaviours of the warp factor and the Higgs field. It is found that the bulk curvature changes the sign around the surface of the wall. We also present some exact solutions for two simple cases: a) the no potential case, b) the cosmological term dominated case. Both solutions have the (naked) curvature singularity. We can regard the domain wall solution as a singularity resolution of the exact solutions.

Conformal anomaly in 4D gravity-matter theories non-minimally coupled with a dilaton

Abstract We present and examine closely the BRS symmetry in the background-field formalism. Yang-Mills theory and pure Einstein gravity are taken as examples. Ward-Takahashi identities between various expectation values on the background-field are obtained. Using those identities we closely examine the Kallosh theorem, which is important in the renormalizability problem. We argue the breakdown of the theorem in the quantum gravity in relation to the regularization effect.