UNIFICATION OF GAUGE COUPLINGS IN A KALUZA-KLEIN THEORY WITH 2 INTERNAL MANIFOLDS

We consider a Kaluza-Klein theory whose ground state is R4 X M X K, wh ere M and K are compact, irreducible, homogeneous-internal manifolds. This is compatible with the existence of the graviton, gauge fields, m assless scalar fields and the absence of the cosmological constant, pr ovided that M and K are odd dimensional, and a dimensionally continued Euler form action whose dimension is the same as the dimension of M X K is chosen. In such a theory, the gauge couplings g(M)2 and g(K)2 ar e unified. For M X K = S2m+1 X S2k+1, g(M)2/g(K)2 = m/k.