  ABRIDGED: Diffuse interstellar bands (DIBs) are faint spectral absorption
features of unknown origin. Research on DIBs beyond the Local Group (LG) will
surely blossom in the era of the ELTs. A possibility that needs to be explored
is the use of integral field spectrographs. We do so by using MUSE data for the
Antennae Galaxy, the closest major galaxy merger. High S-to-N spectra were
created by co-adding the signal of many spatial elements. The emission of the
underlying stellar population was modeled using STARLIGHT. To our knowledge, we
have derived the first maps for the DIBs at l5780 and l5797 in galaxies outside
the LG. The l5780 DIB was detected in an area of ~0.6 arcmin2, corresponding to
a linear scale of ~25 kpc2. This region was sampled using >200 independent
lines of sight. The DIB l5797 was detected in >100 independent lines of sight.
Both DIBs are associated with a region with high emission in the HI 21 cm line,
implying a connection between atomic gas and DIBs, as the correlations for the
Milky Way also suggest. Conversely, there is mild spatial association between
the two DIBs and the molecular gas, in agreement with results for our Galaxy
that indicate a lack of correlation between DIBs and molecular gas. The overall
structure for the DIB strength distribution and extinction are comparable.
Within the system, the l5780 DIB clearly correlates with the extinction. Both
DIBs follow the relationship between equivalent width and reddening when data
for several galaxies are considered. Unidentified Infrared emission Bands
(UIBs, likely caused by PAHs) and the l5780 and l5797 DIBs show similar but not
identical spatial distributions. We attribute the differences to extinction
effects without necessarily implying a radically different nature of the
respective carriers. The results illustrate the enormous potential of integral
field spectrographs for extragalactic DIB research.
