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We argue that, in a theory of quantum gravity, the gauge coupling and theconfinement scale of a gauge theory are related to distance in the space ofmetric configurations, and in turn to the cosmological constant. To support theargument, we compute the gauge kinetic functions in variuos supersymmetricHeterotic and type II string compactifications and show that they depend ondistance. According to the swampland program, the distance between two (anti)de Sitter vacua in the space of metric configurations is proportional to thelogarithm of the ratio of cosmological constants and thus the confinement scaledepends on the value of the cosmological constant. In this framework, for deSitter space, we revisit the swampland Festina Lente bound and gauge theoriesin the dark dimension scenario. We show that if the Festina Lente bound isrealized in a de Sitter vacuum and dependence on distance is strong enough, itwill be realized in vacua with higher cosmological constants. In dark dimensionscenario, as the value of cosmological constant is related to thedecompactifying dimension, we find that the confinement scale is indeed relatedto radius of dark dimension. We show that in this scenario the Festina Lentebound holds for the standard model QCD, as well as all confining gauge groupswith $N_c\lesssim 10^3$.

Confinement from Distance in Metric Space and its Relation to Cosmological Constant