  We have detected, for the first time, Cepheid variables in the Sculptor Group
spiral galaxy NGC 7793. From wide-field images obtained in the optical V and I
bands on 56 nights in 2003-2005, we have discovered 17 long-period (24-62 days)
Cepheids whose periods and mean magnitudes define tight period-luminosity
relations. We use the (V-I) Wesenheit index to determine a reddening-free true
distance modulus to NGC 7793 of 27.68 +- 0.05 mag (internal error) +- 0.08 mag
(systematic error). The comparison of the reddened distance moduli in V and I
with the one derived from the Wesenheit magnitude indicates that the Cepheids
in NGC 7793 are affected by an average total reddening of E(B-V)=0.08 mag, 0.06
of which is produced inside the host galaxy. As in the earlier Cepheid studies
of the Araucaria Project, the reported distance is tied to an assumed LMC
distance modulus of 18.50. The quoted systematic uncertainty takes into account
effects like blending and possible inhomogeneous filling of the Cepheid
instability strip on the derived distance. The reported distance value does not
depend on the (unknown) metallicity of the Cepheids according to recent
theoretical and empirical results. Our Cepheid distance is shorter, but within
the errors consistent with the distance to NGC 7793 determined earlier with the
TRGB and Tully-Fisher methods. The NGC 7793 distance of 3.4 Mpc is almost
identical to the one our project had found from Cepheid variables for NGC 247,
another spiral member of the Sculptor Group located close to NGC 7793 on the
sky. Two other conspicuous spiral galaxies in the Sculptor Group, NGC 55 and
NGC 300, are much nearer (1.9 Mpc), confirming the picture of a very elongated
structure of the Sculptor Group in the line of sight put forward by Jerjen et
al. and others.
