  The directed flow of charged particles at mid-rapidity is measured in Pb-Pb
collisions at $\sqrt{s_\rm{NN}}=2.76$ TeV relative to the collision symmetry
plane defined by the spectator nucleons. A negative slope of the rapidity-odd
directed flow component with approximately 3 times smaller magnitude than found
at the highest RHIC energy is observed. This suggests a smaller longitudinal
tilt of the initial system and disfavors the strong fireball rotation predicted
for the LHC energies. The rapidity-even directed flow component is measured for
the first time with spectators and found to be independent of pseudorapidity
with a sign change at transverse momenta $p_{\rm T}$ between $1.2$ and $1.7$
GeV/$c$. Combined with the observation of a vanishing rapidity-even $p_{\rm T}$
shift along the spectator deflection this is strong evidence for dipole-like
initial density fluctuations in the overlap zone of the nuclei. Similar trends
in the rapidity-even directed flow and the estimate from two-particle
correlations at mid-rapidity, which is larger by about a factor of 40, indicate
a weak correlation between fluctuating participant and spectator symmetry
planes. These observations open new possibilities for investigation of the
initial conditions in heavy-ion collisions with spectator nucleons.
