  In this article we study field-theoretical aspects of multipolar topological
insulators. Previous research has shown that such systems naturally couple to
higher-rank tensor gauge fields that arise as a result of gauging dipole or
subsystem $U(1)$ symmetries. Here we propose a complementary framework using
electric higher-form symmetries. We utilize the fact that gauging 1-form
electric symmetries results in a 2-form gauge field which couples naturally to
extended line-like objects: Wilson lines. In our context the Wilson lines are
electric flux lines associated to the electric polarization of the system. This
allows us to define a generalized 2-form Peierls' substitution for dipoles that
shows that the off-diagonal components of a rank-2 tensor gauge field $A_{ij}$
can arise as a lattice Peierls factor generated by the background antisymmetric
2-form gauge field. This framework has immediate applications: (i) it allows us
to construct a manifestly topological quadrupolar response action given by a
Dixmier-Douady invariant -- a generalization of a Chern number for 2-form gauge
fields -- which makes plain the quantization of the quadrupole moment in the
presence of certain crystal symmetries; (ii) it allows for a clearer
interpretation of the rank-2 Berry phase calculation of the quadrupole moment;
(iii) it allows for a proof of a generic Lieb-Schultz-Mattis theorem for
dipole-conserving systems.
