  In accordance with recent progress of fracton topological phases, unusual
topological phases of matter hosting fractionalized quasiparticle excitations
with mobility constraints, new type of symmetry is studied -- multipole
symmetry, associated with conservation of multipoles. Based on algebraic
relation between dipole and global charges, we introduce a series of
$(d+1)$-dimensional BF theories with $p$-form gauge fields, which admit dipole
of spatially extended excitations, and study their physical properties. We
elucidate that gauge invariant loops have unusual form, containing linear
function of the spatial coordinate, which leads to the position dependent
braiding statistics and unusual ground state degeneracy dependence on the
system size. We also show that the theories exhibit a mixed 't Hooft anomaly
between $p$-form and $(d-p)$-form dipole symmetries, which is canceled by an
invertible theory defined in one dimensional higher via anomaly inflow
mechanism.
