  We discuss nonstandard continuum quantum field theories in 2+1 dimensions.
They exhibit exotic global symmetries, a subtle spectrum of charged
excitations, and dualities similar to dualities of systems in 1+1 dimensions.
These continuum models represent the low-energy limits of certain known lattice
systems. One key aspect of these continuum field theories is the important role
played by discontinuous field configurations. In two companion papers, we will
present 3+1-dimensional versions of these systems. In particular, we will
discuss continuum quantum field theories of some models of fractons.
