Quantum Dynamics of a Bulk-Boundary System

The quantum dynamics of a bulk-boundary theory is closely examined by the use of the background field method. As an example we take the Mirabelli-Peskin model, which is composed of 5D super Yang-Mills (bulk) and 4D Wess-Zumino (boundary). Singular interaction terms play an important role of canceling the divergences coming from the KK-mode sum. Some new regularization of the momentum integral is proposed. An interesting background configuration of scalar fields is found. It is a localized solution of the field equation. In this process of the vacuum search, we present a new treatment of the vacuum with respect to the extra coordinate. The "supersymmetric" effective potential is obtained at the 1-loop full (w.r.t. the coupling) level. This is the bulk-boundary generalization of the Coleman-Weinberg's case. Renormalization group analysis is done where the correct 4d result is reproduced. The Casimir energy is calculated and is compared with the case of the Kaluza-Klein model.Comment: 57 pages,10 figures, final version

CP-Violation in Kaluza-Klein and Randall-Sundrum Theories

The Kaluza-Klein theory and Randall-Sundrum theory are examined comparatively, with focus on the five dimensional (Dirac) fermion and the dimensional reduction to four dimensions. They are treated in the Cartan formalism. The chiral property, localization, anomaly phenomena are examined. The electric and magnetic dipole moment terms naturally appear. The order estimation of the couplings is done. This is a possible origin of the CP-violation.Comment: 3 pages, 2 figures, Proceedings of the Fifth KEK Topical Conference -Frontiers in Flavor Physics

Casimir Energy of the Universe and the Dark Energy Problem

We regard the Casimir energy of the universe as the main contribution to the cosmological constant. Using 5 dimensional models of the universe, the flat model and the warped one, we calculate Casimir energy. Introducing the new regularization, called {\it sphere lattice regularization}, we solve the divergence problem. The regularization utilizes the closed-string configuration. We consider 4 different approaches: 1) restriction of the integral region (Randall-Schwartz), 2) method of 1) using the minimal area surfaces, 3) introducing the weight function, 4) {\it generalized path-integral}. We claim the 5 dimensional field theories are quantized properly and all divergences are renormalized. At present, it is explicitly demonstrated in the numerical way, not in the analytical way. The renormalization-group function (\be-function) is explicitly obtained. The renormalization-group flow of the cosmological constant is concretely obtained.Comment: 12 pages, 13 figures, Proceedings of DSU2011(2011.9.26-30,Beijin

Weak Field Expansion of Gravity: Graphs, Matrices and Topology

We present some approaches to the perturbative analysis of the classical and quantum gravity. First we introduce a graphical representation for a global SO(n) tensor (\pl)^d h_\ab, which generally appears in the weak field expansion around the flat space: g_\mn=\del_\mn+h_\mn. Making use of this representation, we explain 1) Generating function of graphs (Feynman diagram approach), 2) Adjacency matrix (Matrix approach), 3) Graphical classification in terms of "topology indices" (Topology approach), 4) The Young tableau (Symmetric group approach). We systematically construct the global SO(n) invariants. How to show the independence and completeness of those invariants is the main theme. We explain it taking simple examples of \pl\pl h-, {and} (\pl\pl h)^2- invariants in the text. The results are applied to the analysis of the independence of general invariants and (the leading order of) the Weyl anomalies of scalar-gravity theories in "diverse" dimensions (2,4,6,8,10 dimensions).Comment: 41pages, 26 figures, Latex, epsf.st

Casimir Energy of 5D Electro-Magnetism and Sphere Lattice Regularization

Casimir energy is calculated in the 5D warped system. It is compared with the flat one. The position/ momentum propagator is exploited. A new regularization, called {\it sphere lattice regularization}, is introduced. It is a direct realization of the geometrical interpretation of the renormalization group. The regularized configuration is closed-string like. We do {\it not} take the KK-expansion approach. Instead the P/M propagator is exploited, combined with the heat-kernel method. All expressions are closed-form (not KK-expanded form). Rigorous quantities are only treated (non-perturbative treatment). The properly regularized form of Casimir energy, is expressed in the closed form. We numerically evaluate its \La(4D UV-cutoff), \om(5D bulk curvature, warpedness parameter) and $T$(extra space IR parameter) dependence.Comment: 3 pages, 3 figures, Proceedings of WS "Prog. String th. and QFT"(Osaka City Univ., 07.12.7-10

New Approach to Cosmological Fluctuation using the Background Field Method and CMB Power Spectrum

A new field theory formulation is presented for the analysis of the CMB power spectrum distribution in the cosmology. The background-field formalism is fully used. Stimulated by the recent idea of the {\it emergent} gravity, the gravitational (metric) field g_\mn is not taken as the quantum-field, but as the background field. The statistical fluctuation effect of the metric field is taken into account by the path (hyper-surface)-integral over the space-time. Using a simple scalar model on the curved (dS$_4$) space-time, we explain the above things with the following additional points: 1) Clear separate treatment of the classical effect, the statistical effect and the quantum effect; 2) The cosmological fluctuation comes not from the 'quantum' gravity but from the unkown 'microscopic' movement; 3) IR parameter ($\ell$) is introduced for the time axis as the periodicity. Time reversal(Z$_2$)-symmetry is introduced in order to treat the problem separately with respect to the Z$_2$ parity. This procedure much helps both UV and IR regularization to work well.Comment: 6 pages, 5 figures, Presentation at APPC12(Makuhari,Chiba,Japan,2013.7.14-19), JPS Conference Proceedings (in press

Brane-Anti-Brane Solution and SUSY Effective Potential in Five Dimensional Mirabelli-Peskin Model

A localized configuration is found in the 5D bulk-boundary theory on an $S_1/Z_2$ orbifold model of Mirabelli-Peskin. A bulk scalar and the extra (fifth) component of the bulk vector constitute the configuration. \Ncal=1 SUSY is preserved. The effective potential of the SUSY theory is obtained using the background field method. The vacuum is treated in a general way by allowing its dependence on the extra coordinate. Taking into account the {\it supersymmetric boundary condition}, the 1-loop full potential is obtained. The scalar-loop contribution to the Casimir energy is also obtained. Especially we find a {\it new} type which depends on the brane configuration parameters besides the $S_1$ periodicity parameter.Comment: 14 pages, 4 figures, Some points are improve