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  Physical applications of the coset-space E6/Spin(10)×S0(2)

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The coset-space E6/Spin(10)×SO(2) is Hodge manifold which can be imbedded into a complex projective  space.  Please let me know what are the possible physical applications of such coset-space. 

asked Aug 7, 2016 in Theoretical Physics by juancho (1,130 points) [ revision history ]

1 Answer

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In Grand unification theory, E6 appears as a possible gauge group which, after a suitable symmetry breaking, gives rise to  the gauge group of the standard model SU(3)×SU(2)×U(1)

This is achieving via the breaking to Spin(10)×SO(2) and then to SO(10)×U(1) .  According with this, the physical states will appear  in representations of the coset-space  E6/Spin(10)×SO(2).  Explicitly we have that

78450163¯163+10

2714102161


¯2714102¯161

Where the subscript denotes the SO(2) charge. In such way, we can get the Standard Model's elementary fermions and Higgs boson.

Reference (Adaptation from)

http://en.wikipedia.org/wiki/E6_(mathematics)

answered Aug 10, 2016 by juancho (1,130 points) [ revision history ]
edited Aug 10, 2016 by juancho

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