Abstract
We extend the methods of ’t Hooft for the planar model of QCD to their natural supersymmetric generalizations for a pure SUSY Yang-Mills theory with gauge group ℐ. We find, to leading order in the infrared and coupling constant expansions in the respective Dyson-Schwinger and Bethe-Salpeter equations, a massless SUSY multiplet of spins (2,3/2). Following Weinberg, Grisaru and Pendleton, and Kugo and Uehara, we identify this multiplet with the graviton and the gravitino in the spirit of the Sudarshan-Flatoet al. interpretation of the Weinberg-Witten theorem. We propose, therefore, that quantum gravity is really the low-energy remnant of a more fundamental theory: a SUSY Yang-Mills theory with scale parameterΛQSGCD∼MP, whereMP is the Planck mass. The true unification of gravity with the strong, weak and electromagnetic interactions occurs at a scaleMSSU⋍1·1021 GeV in anE8 example, whereE8 is the gauge group of the world. Possible connections with the superstring theories of Green and Schwarz and of Grosset al. are discussed.
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