Supersymmetric theories on squashed five-sphere

We construct supersymmetric theories on the SU(3)xU(1) symmetric squashed five-sphere with 2, 4, 6, and 12 supercharges. We first determine the Killing equation by dimensional reduction from 6d, and use Noether procedure to construct actions. The supersymmetric Yang-Mills action is straightforwardly obtained from the supersymmetric Chern-Simons action by using a supersymmetry preserving constant vector multiplet.Comment: 20 pages, no figure, LaTeX; v3: minor corrections, accepted for publication in PTE

Impact and Implication of Bi-Large Neutrino Mixings on GUTs

Under the assumptions that 1) the quark/lepton mass matrices take Froggatt-Nielsen's factorized power form \lambda^{\psi_i+\psi_j} with anomalous U(1) charges \psi_i, and 2) the U(1) charges \psi_i respect the SU(5) GUT structure, we show that the quark mass data necessarily implies the large 2-3 mixing in the MNS mixing matrix U_{MNS}. If we further add the data of the mass squared difference ratio of solar and atmospheric neutrinos, then, it implies that the 1-2 mixing in U_{MNS} is also large, so explaining the bi-large mixing. This analysis also gives a prediction that U_{e3}\equiv(U_{\rm MNS})_{13} should be of order \lambda \sim (0.1 - 0.5).Comment: 8 pages, uses ws-procs9x6.cls, talk at NOON03 (Kanazawa, Feb. 2003

Supergravity Tensor Calculus in 5D from 6D

Supergravity tensor calculus in five spacetime dimensions is derived by dimensional reduction from the d=6 superconformal tensor calculus. In particular, we obtain an off-shell hypermultiplet in 5D from the on-shell hypermultiplet in 6D. Our tensor calculus still retains the dilatation gauge symmetry so that it becomes a trivial gauge fixing to make the Einstein term canonical in a general matter-Yang-Mills-supergravity coupled system.Comment: 38 pages, no figures, LaTeX, version to appear in PTP 104(2000),835-86

Dynamical Symmetry Breaking in an E_6 GUT Model

Dynamical symmetry breaking is studied in an E_6 GUT model of a single generation of fermions with strong 4-fermi interactions. The effective potential is analyzed analytically by the help of Michel's conjecture and the result is confirmed numerically. We find that the E_6 symmetry is spontaneously broken either to F_4 or to Sp(8) or G_2 or SU(3), depending on which of the 4-fermi coupling constants G_27 and G_351 in the 27/351 channels is stronger. The possibilities for obtaining other type of breaking patterns are also discussed.Comment: 29 pages (no figures), phyzzx and tables.tex KUNS-125

Unoriented Open-Closed String Field Theory

The string field theory for unoriented open-closed string mixed system is constructed up to quadratic order based on the joining-splitting type vertices. The gauge invariance with closed string transformation parameter is proved. The infinity cancellation mechanism between disk and projective plane amplitudes plays an essential role for the gauge invariance of the theory.Comment: 40 pages, LaTeX with PTPTeX.sty, 19 eps figure

Defining the Nambu--Jona-Lasinio Model by Higher Derivative Kinetic Term

Usual treatment of the Nambu--Jona-Lasinio (NJL) model using loop momentum cutoff suffers from ambiguities in choosing the loop momenta to be cut off and violation of (external) gauge invariance. We define the NJL model from the starting Lagrangian level by using a higher derivative fermion kinetic term with a cutoff parameter $\Lambda$. This definition is free from such ambiguities and manifestly keeps the chiral symmetry as well as the gauge invariance. Quantization of this higher derivative system, current operators and calculational method are discussed in some detail. Calculating the pion decay constant and $\pi^0\rightarrow 2\gamma$ decay amplitude, we explicitly demonstrate that the low energy theorem holds. It is observed that the NJL mass relation $m_\sigma = 2 m_0$ between the $\sigma$ meson and fermion masses no longer holds in this model. We also present a simplified calculational method which is valid when the cutoff parameter $\Lambda$ is much larger than the energy scale of physics.Comment: 31 pages, phyzzx, 3 uuencoded epsf figures, KUNS-126

Neutrino Masses in E_6 Unification

We show that the neutrino masses with large mixing between \nu_\mu and \nu_\tau are naturally reproduced in a supersymmetric E_6 grand unification model with an anomalous U(1)_X symmetry. We propose a simple scenario which incorporates a novel mechanism called `E-twisting' by which all the characteristic features of the fermion mass matrices, not only the quark/lepton's Dirac masses but also the neutrino's Majorana masses, can be well reproduced despite all the members in 27 of each generation are assigned a common U(1)_X charge.Comment: 21 pages, 2 eps figures, v2 (almost published version