  In this work we predict the existence of a novel species of Wannier excitons
when exposed to crossed electric and magnetic fields. In particular, we present
a theory of giant-dipole excitons in $\textrm{Cu}_2\rm O$ in crossed fields.
Within our theoretical approach we perform a pseudoseparation of the
center-of-mass motion for the field-dressed excitonic species, thereby
obtaining an effective single-particle Hamiltonian for the relative motion. For
arbitrary gauge fields we exactly separate the gauge-dependent kinetic energy
terms from the effective single-particle interaction potential. Depending on
the applied field strengths and the specific field orientation, the potential
for the relative motion of electron and hole exhibits an outer well at spatial
separations up to several micrometers and depths up to $380\, \mu \rm eV$,
leading to possible permanent excitonic electric dipole moments of around three
million Debye.
