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de Sitter Conjectures in N=1 Supergravity

Supergravity theories at D=4 allow to formulate the Swampland de Sitter conjectures in the complex field space of scalar components of chiral multiplets. We formulate the de Sitter and refined de Sitter conjecture by using the Kähler invariant ${\cal G}$-function and explore a class of models in the Landscape/Swampland scenario which obey and/or violate such conjectures. Furthermore we give a new construction of single exponential potentials in supergravity. These depend on a chiral superfield with a Kähler potential parametrizing an SU(1,1)/U(1) geometry. We show that the construction allows for modifications to supergravity theories causing them to obey the de Sitter conjectures.