Gauge theory with light flavor quark is studied by embedding a D7 brane in a deconfinement phase background newly constructed. We find a phase transition by observing a jump of the vacuum expectation value of quark bilinear and also of the derivative of D7 energy at a critical temperature. For the model considered here, we also study quark-antiquark potential to see some possible quark-bound states and other physical quantities in the deconfinement phase. † gouroku@dontaku.fit.ac.jp

Gauge symmetry breaking by boundary conditions is studied in a general warped geometry in five dimensions. It has been suggested that a wider class of boundary conditions is allowed by requiring only vanishing surface terms when deriving the field equations for gauge theories on an interval (i.e., employing a variational principle), in comparison to the twist in orbifolding with automorphisms of the Lie algebra. We find that there are classes of boundary conditions allowed by the variational principle which violate the Ward-Takahashi identity and give four-point tree amplitudes that increase with energy in channels that have not yet been explored, leading to cross sections that increase as powers of the energy (which violates the tree level unitarity). We also find that such boundary conditions are forbidden by the requirement that the definitions of the restricted class of five-dimensional (5D) gauge transformations be consistent. §1. IntroductionIn models with extra dimensions, there are various possibilities for gauge fields. The initial proposal for the large extra dimensions assumes that all particles in the standard model are localized on a brane with a four-dimensional (4D) world volume. 1)−4) Formulating the localization of gauge fields on a wall is a challenging problem, which can be realized in certain models. 5),6) However, other interesting possibilities arise if the gauge fields are propagating in the higher-dimensional bulk spacetime. The extra-dimensional component of gauge fields can act as a Higgs scalar field to break the gauge symmetry. 7) The Wilson line dynamics can provide another source of gauge symmetry breaking, namely, the Hosotani mechanism. 8) If the extra dimensions are compactified on a topologically nontrivial manifold, such as S 1 , twisting can be realized, and the Scherk-Schwarz symmetry breaking mechanism thereby appears. 9) The key to these mechanisms can be summarized as a nontrivial holonomy along a nontrivial cycle, which can also be understood as vacuum expectation values of adjoint scalar fields coming from gauge field components along the extra dimensions. If orbifolds are introduced, one can also impose boundary conditions at the fixed points of the orbifold to break all or part of a gauge group, usually using the automorphisms of the Lie algebra. 10)−15) Combined with the Wilson lines, the orbifold models have recently gained much attention. 16)−20) A class of boundary conditions wider than the orbifolding with automorphisms has been pursued to obtain more realistic models, in particular, to reduce the rank of the gauge group. 12) One notable proposal is to consider gauge theories on an interval and to require * ) E-mail: nsakai@th.phys.titech.ac.jp * * ) E-mail: uekusa@th.phys.titech.ac.jp 2 Norisuke Sakai and Nobuhiro Uekusa that the surface terms must vanish in order for the variational principle 21) to give field equations. * ) By imposing boundary conditions, part of the five-dimensional (5D) gauge invariance is explicitly broken, although the 5D gauge invariance ...

The electroweak currents of quarks and leptons in the SO(5) × U (1) gauge-Higgs unification model in the Randall-Sundrum warped space are determined. The 4D gauge couplings deviate from those in the standard model and the weak universality is slightly violated. It is shown that the model is free from 4D anomalies and the deviations of the gauge couplings are tiny, less than 1% except for the top quark. The Zt LtL , Zt RtR , Zb LbL and Zb RbR couplings deviate from those in the standard model by −7%, 18%, 0.3% and 0.9% with the warp factor z L = 10 15 , respectively. The violation of the μ-e, τ -e and t-e universality in the charged current interactions is O(10 −8 ), O(10 −6 ) and 2.3%, respectively. Subject Index: 101, 131, 133, 143, 150 §1. IntroductionThe Higgs boson is the only particle yet to be found in the standard model of electroweak interactions. It is not clear, however, if the Higgs boson appears as described in the standard model. New physics may be hidden behind it.In the gauge-Higgs unification scenario the 4D Higgs field is identified with a part of the extra-dimensional component of gauge fields in higher dimensions. 1), 2) The 4D Higgs field appears as an Aharonov-Bohm (AB) phase, or a Wilson line phase, in the extra dimension. 3)-5) The electroweak (EW) symmetry breaking is induced by dynamics of the AB phase through the Hosotani mechanism. A finite mass of the Higgs boson is generated at the quantum level, the mechanism of which provides a new way of solving the gauge hierarchy problem as an alternative to supersymmetric theories, the little Higgs model and the Higgsless model. 6) A realistic gauge-Higgs unification model is constructed in the Randall-Sundrum warped space. 7)-9) Based on the gauge group SO(5) × U (1) quarks and leptons are introduced in the vector (5) representation of SO(5) in the bulk five-dimensional spacetime with additional fermions localized on the Planck brane. 10)-13) The presence of the top quark dynamically induces the EW symmetry breaking, thereby the effective potential V eff for the AB phase θ H being minimized at θ H = ± 1 2 π. 12) In the gauge-Higgs unification scenario the interactions of the Higgs boson are governed by the gauge principle. Its interactions with other particles deviate from those in the standard model, which may be understood as manifestation of the underlying gauge invariance.

In the SOð5Þ Â Uð1Þ gauge-Higgs unification model in the Randall-Sundrum warped space, there results the conservation of the H parity. The H parity is assigned to all 4D fields including excited modes in Kaluza-Klein towers. The neutral Higgs boson is the lightest particle of odd H parity, consequently becoming absolutely stable. Its mass is found to be 70-135 GeV for the warp factor z L ¼ 10 5 -10 15 .

Supersymmetry breaking and radius stabilization by constant superpotentials localized at boundaries is studied in a supersymmetric warped space model where a hypermultiplet, a compensator and a radion multiplet are taken into account. Soft mass induced by the anomaly mediation can be of the order of 100GeV and can be dominant compared to that mediated by bulk fields. A lighter physical mode composed of the radion and the moduli can have mass of the order of a TeV and the gravitino mass can be of the order of 10 7 GeV. The radius is stabilized by the presence of the constant boundary superpotentials. We also find that the mass splitting has an interesting dependence on the bulk mass parameter c.