  The duality between a higher curvature $f(R)$ gravity model and a
scalar-tensor theory helps to bring out the role of the additional degree of
freedom originating from the higher derivative terms in the gravity action.
Such a degree of freedom which appears as a scalar field has been shown to have
multiple implications in Cosmological/Astrophysical scenario. The present work
proposes a novel generalization to this correspondence between $f(R)$ gravity
and a dual scalar-tensor theory when the affine connection is considered to
have an antisymmetric part. It turns out that the $f(R)$ action in presence of
spacetime torsion can be recast to a $non-minimally$ coupled scalar-tensor
theory with a 2-rank massless antisymmetric tensor field in the Einstein frame,
where the scalar field gets coupled with the antisymmetric field through
derivative coupling(s).
