String universality in ten dimensions

TL;DR

The paper investigates whether ten-dimensional ${\cal N}=1$ supergravity with abelian gauge factors can be a consistent quantum theory. It analyzes anomaly cancellation through the Green-Schwarz mechanism and the factorization of the anomaly polynomial $\hat{I}_{12}$, distinguishing abelian from non-abelian sectors. It finds that while non-abelian theories like $SO(32)$ and $E_8 \times E_8$ are anomaly-free and align with string theory, the abelian candidates $U(1)^{496}$ and $E_8 \times U(1)^{248}$ face a fundamental obstruction: abelian gauge invariance cannot be preserved if the Green-Schwarz term $\int B_2 \wedge X_8$ is used to cancel gravitational anomalies, since there is no abelian anomaly to cancel the required $U(1)$ variation of $B_2$. Consequently, these abelian theories cannot be consistent quantum theories of gravity in ten dimensions, supporting the notion of string universality in this setting.

Abstract

We show that the ${\cal N}=1$ 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.

Figures (1)

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