The methods of supergravity allow us to derive a multi-field F-term potential. Using this, we denote a generic and non-positive single-field F-term potential. We insert our theory into the scalar-gravity part of the (2,1|1) invariant superconformal action. That action leads us to a de Sitter solution at the inflationary trajectory. One can denote stabilization of fields in terms of the Kähler kinetic terms and single-field slow-roll inflation parameters. We combine these with the de Sitter swampland conjecture to generate a bounded conjecture. This approach allowed us to show that the single field slow-roll inflation works in harmony with bounded de Sitter conjecture for any concave inflation potential.

We provide a tensor calculus for n-number of $${\mathcal {N}}= (1,0)$$ N = ( 1 , 0 ) linear multiplets in six dimensions. The coupling of linear multiplets is encoded in a function $${\mathcal {F}}_{IJ}$$ F IJ that is subject to certain constraints. We provide various rigid and local supersymmetric models depending on the choice of the function $${\mathcal {F}}_{IJ}$$ F IJ and provide an interesting off-diagonal superinvariant, which leads to an $$R^2$$ R 2 supergravity upon elimination of auxiliary fields.