On U-Folds and Their Construction

We review a general paradigm for constructing U-fold backgrounds in (dimensionally reduced) Type IIB superstring theory, of the form ${\mathrm{A}\mathrm{d}\mathrm{S}}_{d-1}\times S^1\times S^d$, with a monodromy along $S^1$ in the string-duality group. We also consider a special instance with $d=3$ in Type IIB superstring theory, discuss its ten-dimensional uplift and assess its supersymmetry.