Quantization of the Gauge Coupling Constant in a Five-Dimensional Yang-Mills-Einstein Supergravity Theory

Abstract

We construct the five-dimensional ($d=5$) Yang-Mills-Einstein supergravity with noncompact gauge group SU(3,1). This model is a unified theory in the sense that there is a symmetry connecting each field to all the others, and it is the unique $d=5$ Yang-Mills-Einstein supergravity theory with this property. We show that consistency of the quantum theory requires the dimensionless product ${\ensuremath{\kappa}}^{\ensuremath{-}1}{g}^{s}$ of gravitational constant and gauge coupling constant to be quantized.