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An SU(4) extrapolation of the chiral unitary theory in coupled channels doneto study the scalar mesons in the charm sector is extended to produce resultsin finite volume. The theory in the infinite volume produces dynamically the$D_{s^*0}(2317)$ resonance by means of the coupled channels $KD$, $\eta D_s$.Energy levels in the finite box are evaluated and, assuming that they wouldcorrespond to lattice results, the inverse problem of determining the boundstates and phase shifts in the infinite volume from the lattice data isaddressed. We observe that it is possible to obtain accurate $KD$ phase shiftsand the position of the $D_{s^*0}(2317)$ state, but it requires the explicitconsideration of the two coupled channels in the analysis if one goes close tothe $\eta D_s$ threshold. We also show that the finite volume spectra lookrather different in case the $D_{s^*0}(2317)$ is a composite state of the twomesons, or if it corresponds to a non molecular state with a small overlap withthe two meson system. We then show that a careful analysis of the finite volumedata can shed some light on the nature of the $D_{s^*0}(2317)$ resonance as a$KD$ molecule or otherwise.

The $KD$, $\eta D_s$ interaction in finite volume and the nature of the $D_{s^* 0}(2317)$ resonance