We consider a notion of fractional s-area for codimension 2 surfaces in a closed Riemannian manifold or the Euclidean space, which can be seen as an extension of the fractional perimeter to higher codimension. The definition involves a minimum problem over a class of circle-valued maps having prescribed singularities on the given surface. We discuss various properties of the s-area when s is fixed, and we show that when s tends to 1 it Gamma-converges, with coercivity, to the classical area in the framework of currents. The talk is based on a joint project with Michele Caselli and Mattia Freguglia. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027).