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A 6-dimensional grand unified theory with the compact space having the topology of a real projective plane, i.e., a 2-sphere with opposite points identified, is considered. The space is locally flat except for two conical singularities where the curvature is concentrated. One supersymmetry is preserved in the effective 4d theory. The unified gauge symmetry, for example SU(5) , is broken only by the non-trivial global topology. In contrast to the Hosotani mechanism, no adjoint Wilson-line modulus associated with this breaking appears. Since, locally, SU(5) remains a good symmetry everywhere, no UV-sensitive threshold corrections arise and SU(5)-violating local operators are forbidden. Doublettriplet splitting can be addressed in the context of a 6d N = 2 super Yang-Mills theory with gauge group SU(6). If this symmetry is first broken to SU(5) at a fixed point and then further reduced to the standard model group in the above non-local way, the two light Higgs doublets of the MSSM are predicted by the group-theoretical and geometrical structure of the model.

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The paper considers advantages and special features of an acousto-optic method for the development of a functional device for spatial and temporal control of laser light and reports results of investigations to create a two-directional acousto-optic laser scanner with diffraction efficiency as high as 80 percent or better. An acousto-optic deflector on a paratellurite crystal operating under the Bragg diffraction condition with a lithium niobate piezoelectric acoustic transducer was developed and tested experimentally. The results of this work can serve as a basis for the development of prototype functional acousto-optic devices for spatial and temporal control of laser light and their application to create laser television images.