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 o