String Universality in Ten Dimensions

We show that the $\mathcal{N}=1$ supergravity theories in ten dimensions with gauge groups $U(1{)}^{496}$ and $E_8\times U(1{)}^{248}$ are not consistent quantum theories. Cancellation of anomalies cannot be made compatible with supersymmetry and Abelian gauge invariance. Thus, in ten dimensions all supersymmetric theories of gravity without known inconsistencies are realized in string theory.

Figure 1

Green-Schwarz-type tree diagram arising in $\mathcal{N}=1$ supergravity theories in ten dimensions with Abelian factors. With no corresponding anomaly to cancel, these theories are not gauge invariant.