Selecting Gauge Theories on an Interval by 5D Gauge Transformations

Abstract

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 ...

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