gauge multiplet in ten dimensions to four dimensions: where the left hand side of (2.2) is defined in ten dimensions with one supersymmetry generator ( N = 1), and the right hand side is defined in four dimensions, with four supersymmetry generators ( N = 4). The A µ are gauge fields, Ψ are gauginos, and λ represent complex scalars. Six of the ten-dimensional gauge field degrees of freedom become the three complex scalars in the four-dimensional reduction. The one-loop β function for this theory is with the first term coming from the gauge fields, the second from the gaugi- nos, and the third from the scalar fields. Supersymmetric non-renormalization theorems [53] can be used to show that there are no higher order contri- butions to the β function, and thus it is zero for the full quantum theory. A theory which has no massive fields, and whose coupling constant doesn’t undergo dimensional transmutation, is a conformal field theory (CFT). This means the theory is invariant to rescalings of the metric. To conclude: on the string side, we have two decoupled systems: ten- dimensional supergravity; and an SU ( N ) conformal gauge theory. 36 β = ( 11 3 N − 8 3 N − N ) = 0 (2.3)    A µ Ψ    ︸ ︷︷ ︸ D=10 , N =1 −→    A µ Ψ       λ Ψ       λ Ψ       λ Ψ    ︸ ︷︷ ︸ D=4 , N =4 (2.2)