  We measure the weak lensing shear around galaxy troughs, i.e. the radial
alignment of background galaxies relative to underdensities in projections of
the foreground galaxy field over a wide range of redshift in Science
Verification data from the Dark Energy Survey. Our detection of the shear
signal is highly significant (10 to 15$\sigma$ for the smallest angular scales)
for troughs with the redshift range z in [0.2,0.5] of the projected galaxy
field and angular diameters of 10 arcmin...1{\deg}. These measurements probe
the connection between the galaxy, matter density, and convergence fields. By
assuming galaxies are biased tracers of the matter density with Poissonian
noise, we find agreement of our measurements with predictions in a fiducial
Lambda cold dark matter model. The prediction for the lensing signal on large
trough scales is virtually independent of the details of the underlying model
for the connection of galaxies and matter. Our comparison of the shear around
troughs with that around cylinders with large galaxy counts is consistent with
a symmetry between galaxy and matter over- and underdensities. In addition, we
measure the two-point angular correlation of troughs with galaxies which, in
contrast to the lensing signal, is sensitive to galaxy bias on all scales. The
lensing signal of troughs and their clustering with galaxies is therefore a
promising probe of the statistical properties of matter underdensities and
their connection to the galaxy field.
