Abstract
A gauge theory with gauge group G defined in D>4 space–time dimensions can be broken to a subgroup H on four-dimensional fixed point branes, when compactified on an orbifold. Mass terms for extra-dimensional components of gauge fields Ai (brane scalars) might acquire (when allowed by the brane symmetries) quadratically divergent radiative masses and thus jeopardize the stability of the four-dimensional theory. We have analyzed Z2 compactifications and identified the brane symmetries remnants of the higher-dimensional gauge invariance. No mass term is allowed for D=5 while for D>5 a tadpole ∝Fijα can appear when there are Uα(1) factors in H. A detailed calculation is done for the D=6 case and it is established that the tadpole is related, although does not coincide, with the Uα(1) anomaly induced on the brane by the bulk fermions. In particular, no tadpole is generated from gauge bosons or fermions in real representations.
Highlights
A gauge theory with gauge group G defined in D > 4 space–time dimensions can be broken to a subgroup H on fourdimensional fixed point branes, when compactified on an orbifold
No mass term is allowed for D = 5 while for D > 5 a tadpole ∝ Fiαj can appear when there are Uα(1) factors in H
A detailed calculation is done for the D = 6 case and it is established that the tadpole is related, does not coincide, with the Uα(1) anomaly induced on the brane by the bulk fermions
Summary
The gauge parameters ξ a are even fields and ξ aare odd They couple to the branes according to (7). Where LD is given by (1) and Lb4rane should be the most general Lagrangian consistent with the symmetries The latter can be nothing but the original bulk symmetry (2) modded out by the orbifold action and subsequently evaluated at the location of the brane. There is an infinite number of non-zero independent fields on the brane, i.e., ∂2k{Aaμ, Aai } and ∂2k+1{Aaμ , Aai }, and an infinite number of corresponding transformation parameters {∂2kξ a} and {∂2k+1ξ a } induced by the. Given a set of H-covariant objects, invariance under δK is a sufficient condition for their square to be invariant under both δH and δK and to be an allowed terms in the effective action. At the renormalizable level the following terms can appear in the Lagrangian: Lb4rane
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