Non-geometric vacua of the Spin(32)/ℤ 2 heterotic string and little string theories

We study a class of 6d N = (1, 0) non-geometric vacua of the Spin(32)/ℤ2 heterotic string which can be understood as fibrations of genus-two curves over a complex one-dimensional base. The 6d N = (1, 0) theories living on the defects that arise when the genus-two fiber degenerates at a point of the base are analyzed by dualizing to F-theory on elliptic K3-fibered non-compact Calabi-Yau threefolds. We consider all possible degenerations of genus-two curves and systematically attempt to resolve the singularities of the dual threefolds. As in the analogous non-geometric vacua of the E8 × E8 heterotic string, we find that many of the resulting dual threefolds contain singularities which do not admit a crepant resolution. When the singularities can be resolved crepantly, we determine the emerging effective theories which turn out to be little string theories at a generic point on their tensor branch. We also observe a form of duality in which theories living on distinct defects are the same.