Higher-dimensional unification
P. Freund · Cambridge University Press eBooks · 1986
Consider two interesting four-dimensional supersymmetric theories which we have encountered before: the maximal N = 4 Yang–Mills theory, and the maximal N = 8 supergravity theory. Both these theories have remarkable properties: the N = 4 Yang–Mills theory is finite, the N = 8 supergravity solves the matter/force problem (it also may have improved convergence properties). Yet, as is clear from table 5.1 both these theories have rich particle spectra, and complicated lagrangians describe the manifold interactions of these numerous fields. For N = 8 supergravity we even recorded the existence of various forms of the theory (Cremmer–Julia, de Wit–Nicolai, etc…). Somehow this all flies in the face of an unwritten rule of theoretical physics, namely that important theories be simple, unique and beautiful. Could it be that the apparent aesthetic flaws of these theories, are consequences of our way of looking at them, rather than of the theories themselves? What I have in mind is something like looking at an animal outside of its natural habitat when it can easily appear clumsy and weird. Only replacing it on its home ground will reveal its natural grace. What is the natural habitat of these theories? Take the N = 4 supersymmetric Yang–Mills theory in four space–time dimensions. Its particle spectrum involves all massless particles in the adjoint representation of the gauge group G ; dim G spin one particles (each with two transverse degrees of freedom), 6dim G scalars and 4dim G spin one-half Majorana particles (two degrees of freedom each), a total of 8dim G Bose degrees of freedom and 8dim G Fermi degrees of freedom.