Kavli Affiliate: Yuji Tachikawa
| First 5 Authors: Katrin Becker, Katrin Becker, , ,
| Summary:
There exists a rare class of R-symmetry gauged $N=(1,0)$ supergravities in
six dimensions with gauge group $Gtimes U(1)_R$, where $G$ is semisimple with
rank greater than one, and the number of tensor multiplets $n_T=1$, which are
free from all local anomalies. We find new members of this family, in which $G$
contains up to four factors. We study the global anomalies of these models in a
framework in which the Dirac quantization of the anomaly coefficients and the
well-definedness of the Green-Schwarz anomaly counterterm in generic
backgrounds play key roles, and we apply the anomaly freedom criteria that
takes this into account as formulated by Monnier and Moore in
citeMonnier:2018nfs. To this end we use the result derived by Yuji Tachikawa
in the appendix which states that the spin cobordism group $Omega_7^rm
Spin(BG)$ vanishes for $G=G_1times cdots times G_n$ where $G_i$ is $U(1)$
or any simple simply-connected non-Abelian compact Lie group. We also require
correct sign for the vector field kinetic terms, and positive Gauss-Bonnet
term. We find that among the models considered here only one of them fails to
satisfy all the stated criteria. We also find that, in general, the requirement
that the anomaly coefficients defined by the factorized anomaly polynomial are
elements of a unimodular charge lattice imposes a constraint on the number of
vector multiplets given by $n_V=8 rm mod 12$ for $U(1)_R$, and $n_V
= 60$ for $Sp(1)_R$ gauged models.
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