QCD, Flavor, and the de Sitter Swampland

Abstract: The refined swampland de Sitter conjecture (SdSC) is a proposed constraint on the form of the total potential in a theory including quantum gravity. According to this conjecture potentials possessing metastable de Sitter vacua are in the swampland of effective field theories that cannot descend from a theory with gravity. It is known that in the Standard Model (SM), as the quark masses and theta-parameter are varied, IR- calculable metastable states in QCD appear (for N > 2 light quarks) and we discuss in detail their properties. We argue that the SdSC excludes the values of quark masses and theta for which these metastable states can arise, leading to a possible surprising connection between quantum gravity and aspects of low-energy flavor phenomenology. The observed values of the quark masses and QCD theta-parameter are consistent with the SdSC, giving mild indirect support for the conjecture. If, in addition, as partially indicated by large-N c and semi-classical analysis, pure SU (3) Yang-Mills theory has metastable states at theta = 0 (this to our knowledge is not known) then much of the a-priori SM parameter space is eliminated. In particular the limit of large electroweak vacuum expectation v_EW > 50 TeV is excluded by the SdSC if quark Yukawa couplings are kept fixed, possibly shedding a new light on the hierarchy problem. We argue that these statements are robust against the addition of a quintessence field unless extreme fine-tuning is allowed.