Abstract
We construct a supersymmetric grand unified model in the framework of a latticized extra dimension. The SU(5) symmetries on the lattice are broken by the vacuum expectation values of the link fields connecting adjacent SU(5) sites, leaving just the MSSM at low energies. Below the SU(5) breaking scale, the theory gives rise to a similar spectrum as in orbifold breaking of SU(5) symmetry in 5 dimensions, and shares many features with the latter scenario. We discuss gauge coupling unification and proton decay emphasizing the differences with respect to the usual grand unified theories. Our model may be viewed as an effective four dimensional description of the orbifold symmetry breaking in higher dimensions.
Highlights
ÍÌ ÖÒ Ø ÓÒØ ÒÙÙÑ Ð Ñ Ø Ø × × ÕÙ Ú Ð ÒØ ØÓ Ø Ï Ð×ÓÒ Ð Ò Ö Ò Û × Ò × ÓÛÒ ØÓ ÕÙ Ú Ð ÒØ ØÓ Ø ÓÖ ÓÐ Ö Ò Ò Ø ÓÒØ ÒÙÙÑ Ø ÓÖÝ 1⁄2¿ ̧ 1⁄2 ̧ 1⁄2 o ÁÒ Ø × ÑÓ Ð Ø ËÍ¿μ ËÍ3⁄4μ Ò Í1⁄2μ Ù ÓÙÔÐ Ò × Ö ØÖÙÐÝ ÙÒ ¬ Ø ×ÓÑ × Ð o Ï Û ÐÐ ¬Ò Ø Ø Ø ×Ô ØÖÙÑ Ó Ø ÓÒØ ÒÙÙÑ Ø ÓÖÝ × Ö ÔÖÓ ÙÒØÐÑØÓÐÖ ÒÙÑ Ö Ó Ð ØØ ÔÓ ÒØ×o Ï Û ÐÐ Ð×Ó × Ù×× Ö Ð Ø ××Ù × ×Ù × ÓÙ Ð Ø1ØÖ ÔÐ Ø ×ÔÐ ØØ Ò Ò Ù ÓÙÔÐ Ò ÙÒ ¬ Ø ÓÒ Ò Ø × 1 Ñ Ò× ÓÒ Ð Ô ØÙÖ o Ï Ð ¬Ò × Ò Ø × ÛÓÖ Û Ð ÖÒ Ø Ø × Ñ Ð Ö × Ò ÔÙÖ×Ù Ý o × ̧ o o ÃÖ × ̧ Ò Âo Ì ÖÒ Ò 1⁄2 o.
Ï Û ÐÐ Ò Û Ø ×ÙÔ Ö×ÝÑÑ ØÖ ËÍμ Ø ÓÖÝ ÓÒ Ð ØØ Þ ÜØÖ Ñ ÒØ ÓÒo Ï ××ÙÑ ØØÛÚÆ · 1⁄2 ËÍμ Ù ÖÓÙÔ× Û Ø ÓÑÑÓÒ Ù ÓÙÔÐ Ò Û Ø Æ · 1⁄2 Æ 1⁄2 Ú ØÓÖ ÑÙÐØ ÔÐ Ø× Î 1⁄4 ¡ ¡ ¡ Æμ ÓÒ ÓÖ ËÍμo Ì Ö Ö Ð×Ó ØÛÓ × Ø× Ó Æ Ö Ð ÑÙÐØ ÔÐ Ø× ̈ Ò ̧ ̈ ÓÖÑ× ́ 1⁄2 μ ÙÒ Ö Ø ØÛÓ Ò Ö ×Ø ËÍμ3× ̧ Û Ð × Ø ÓÔÔÓ× Ø Ö ×oÌÄÖÒÒ ÓÖ Ø Ú ØÓÖ ÑÙÐØ ÔÐ Ø× Ò Ø Ö Ð ¬ Ð × × Ø ÓÐÐÓÛ Ò
ÕÙ Ö Ö ÓÖ1⁄2 ÓÖ × ÑÔÐ ØÝ Ò × Ó ÓÑÔ Ö ×ÓÒ Û Ø Ø Ö ×ÙÐØ Ó ÓÖ ÓÐ Ö Ò Ò Û ××ÙÑ Ø Ø Ø Ù ÓÙÔÐ Ò × ÒØÐÒÎÎ3× Ö Ø × Ñ ÓÖ ÐÐ Ð ØØ ÔÓ ÒØ×o.
Summary
Ò Ø ÓÒØ ÒÙÙÑ Ð Ñ Ø Ø × × ÕÙ Ú Ð ÒØ ØÓ Ø Ï Ð×ÓÒ Ð Ò Ö Ò Û × Ò × ÓÛÒ ØÓ ÕÙ Ú Ð ÒØ ØÓ Ø ÓÖ ÓÐ Ö Ò Ò Ø ÓÒØ ÒÙÙÑ Ø ÓÖÝ 1⁄2¿ ̧ 1⁄2 ̧ 1⁄2 o ÁÒ Ø × ÑÓ Ð Ø ËÍ¿μ ËÍ3⁄4μ Ò Í1⁄2μ Ù ÓÙÔÐ Ò × Ö ØÖÙÐÝ ÙÒ ¬ Ø ×ÓÑ × Ð o Ï Û ÐÐ ¬Ò Ø Ø Ø ×Ô ØÖÙÑ Ó Ø ÓÒØ ÒÙÙÑ Ø ÓÖÝ × Ö ÔÖÓ ÙÒØÐÑØÓÐÖ ÒÙÑ Ö Ó Ð ØØ ÔÓ ÒØ×o Ï Û ÐÐ Ð×Ó × Ù×× Ö Ð Ø ××Ù × ×Ù × ÓÙ Ð Ø1ØÖ ÔÐ Ø ×ÔÐ ØØ Ò Ò Ù ÓÙÔÐ Ò ÙÒ ¬ Ø ÓÒ Ò Ø × 1 Ñ Ò× ÓÒ Ð Ô ØÙÖ o Ï Ð ¬Ò × Ò Ø × ÛÓÖ Û Ð ÖÒ Ø Ø × Ñ Ð Ö × Ò ÔÙÖ×Ù Ý o × ̧ o o ÃÖ × ̧ Ò Âo Ì ÖÒ Ò 1⁄2 o. Ï Û ÐÐ Ò Û Ø ×ÙÔ Ö×ÝÑÑ ØÖ ËÍμ Ø ÓÖÝ ÓÒ Ð ØØ Þ ÜØÖ Ñ ÒØ ÓÒo Ï ××ÙÑ ØØÛÚÆ · 1⁄2 ËÍμ Ù ÖÓÙÔ× Û Ø ÓÑÑÓÒ Ù ÓÙÔÐ Ò Û Ø Æ · 1⁄2 Æ 1⁄2 Ú ØÓÖ ÑÙÐØ ÔÐ Ø× Î 1⁄4 ¡ ¡ ¡ Æμ ÓÒ ÓÖ ËÍμo Ì Ö Ö Ð×Ó ØÛÓ × Ø× Ó Æ Ö Ð ÑÙÐØ ÔÐ Ø× ̈ Ò ̧ ̈ ÓÖÑ× ́ 1⁄2 μ ÙÒ Ö Ø ØÛÓ Ò Ö ×Ø ËÍμ3× ̧ Û Ð × Ø ÓÔÔÓ× Ø Ö ×oÌÄÖÒÒ ÓÖ Ø Ú ØÓÖ ÑÙÐØ ÔÐ Ø× Ò Ø Ö Ð ¬ Ð × × Ø ÓÐÐÓÛ Ò
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