More anomaly-free models of six-dimensional gauged supergravity

TL;DR

The work demonstrates that six-dimensional ${\cal N}=(1,0)$ gauged supergravity with gauge groups formed from $U(1)$ and $SU(2)$ admits a vast set of anomaly-free models, including many with diagonal gauging of the R-symmetry that can yield flat directions. Local anomaly cancellation is analyzed via Green-Schwarz factorization, encoded in an anomaly matrix $\beta_{ij}$ with rank at most 2, along with explicit conditions for cases like $G_R = U(1)_R$, $U(1)_{R+}$, and $Sp(1)_R$, while global anomalies are treated for groups with nontrivial $\pi_6$, with detailed conditions involving $C_4$ and $D_4$ invariants. A large-scale computer search uncovers enormous numbers of solutions, including over $4\times 10^{7}$ for $U(1)_R \times U(1)$ without drones and numerous abelian configurations with $n_H$, $n_V$ tuned to satisfy factorization, as well as hundreds to thousands of non-Abelian models subject to global anomaly constraints; an extra example with $U(1)_R \times SU(3)$ is also highlighted. The results suggest a richer landscape of consistent 6D models than previously recognized and point to potential connections with string compactifications, higher-dimensional phenomenology, and diagonally gauged scenarios enabling flat directions.

Abstract

We construct a huge number of anomaly-free models of six-dimensional N = (1,0) gauged supergravity. The gauge groups are products of U(1) and SU(2), and every hyperino is charged under some of the gauge groups. It is also found that the potential may have flat directions when the R-symmetry is diagonally gauged together with another gauge group. In an appendix, we determine the contribution to the global SU(2) anomaly from symplectic Majorana Weyl fermions in six dimensions.