N=8 Supergravity + 48 x N=4 Super-Yang-Mills = E8 Symmetry?


It occurs to me there is a way in which this theory can be extended to give an even more symmetric theory which would have E8 symmetry.

The way this would work would be to couple 48 N=4 Super Yang-Mills fields to N=8 Supergravity. (These 48 fields might form a gauge group of SU(7) or O(10)xSU(2) or SU(5)xSU(5) for example - which, coincidentally, are quite nice for phenomenology.) 

The resulting theory would have 256+16*48 = 1024 = 2^10 massless fields (the same as a hypothetical N=10 theory but with all spins<=2).  This theory would have 56+4*48 = 248 massless spin 1/2 fermions of each helicy suggesting an E8 representation may be possible. Pure N=8 Supergravity had 56 massless spin 1/2 fermions (suggesting an E7 representation).

This theory is midway between pure N=8 Supergravity and the lowest energy limit of Heterotic String Theory in 4 dimensions (which has an E8xE8 Super Yang-Mills gauge group). Other interesting theories might be found by adding one of 16, 112 or 240 N=4 Super Yang-Mills fields to N=8 Supergravity and still have a power of 2 for the number of bosons/fermions which seems to be important for the superalgebra to work. For example the 240 could be O(16)xO(16). Although these other theories don't look as if they would have any interesting internal symmetries like E8.

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