One of the most important implications of the Swampland conjectures is the finiteness of the set of consistent theories of quantum gravity.
For theories with a large amount of supersymmetry - those with 32 and 16 supercharges - a full classification of consistent supergravity spectra has been performed and supports the finiteness claim based on the Swampland arguments. For theories with less supersymmetry, there are much weaker constraints which make it more challenging to argue for the boundedness of spectra.
A broad class of supergravity theories with 8 supercharges (in various even dimensions) is obtained by compactifications of F-Theory on elliptically fibred Calabi-Yau manifolds. This additional input allows to use tools from algebraic geometry to bound the number of multiplets appearing in the corresponding supergravity theories.
Based on the pioneering work 2507.06317 by Birkar and Lee, we aim to give a mathematical proof for a saturated bound for consistent spectra of 6D N=(1,0) supergravity theories as well as a generalization thereof to 4D N=1 supergravity theories.