Carlo Branchina - UV-sensitivity in Kaluza Klein Theories: Naturalness and Dark Dimension

When the Higgs potential or the vacuum energy are derived in the framework of Higher dimensional effective field theories on a multiply connected spacetime with compact dimensions and non-trivial boundary conditions (as in the case of the Scherk-Schwarz SUSY breaking), the usual calculations lead to the conclusion that these quantities are naturally UV-insensitive. By means of a thorough analysis of the assumptions on which these calculations are based, I will show that this paradigm actually misses a crucial source of UV-sensitivity, ultimately connected to the non-trivial topology of the spacetime in these theories. As a consequence, the conclusions on the UV-insensitivity of the Higgs mass, of the Higgs potential, and on the existence of a Dark Dimension (that crucially depends on the supposed UV-insensitivity of the vacuum energy in Kaluza-Klein theories) need to be seriously reconsidered. Our results were challenged in a note very recently posted online. If time allows, I will point out the flaws in these criticisms.