Supergravity theories in more than four dimensions with grand unified gauge symmetries are an important intermediate step towards the ultraviolet completion of the Standard Model in string theory. Using toric geometry, we classify and analyze six-dimensional F-theory vacua with gauge group SO(10) taking into account Mordell-Weil U(1) and discrete gauge factors. Purely from geometry we compute all matter multiplicities and confirm the cancellation of gauge and gravitational anomalies independent of the base space.
References:
W. Taylor, TASI lectures 1104.2051
W. Buchmuller, M. Dierigl, P. Oehlmann and F. Ruehle, arXiv:1709.06609
