  Gauge theories with no Maxwell term are investigated in various setups. The
dynamical generation of the Maxwell term is correlated to the scale invariance
properties of the system. This is discussed mainly in the cases where the gauge
coupling carries dimensions. The term is generated when the theory contains a
scale explicitly, when it is asymptotically free and in particular also when
the scale invariance is spontaneously broken. The terms are not generated when
the scale invariance is maintained. Examples studied include the large $N$
limit of the $CP^{N-1}$ model in $(2+\epsilon)$ dimensions, a 3D gauged
$\phi^6$ vector model and its supersymmetric extension. In the latter case the
generation of the Maxwell term at a fixed point is explored. The phase
structure of the $d=3$ case is investigated in the presence of a Chern-Simons
term as well. In the supersymmetric $\phi^6$ model the emergence of the Maxwell
term is accompanied by the dynamical generation of the Chern-Simons term and
its multiplet and dynamical breaking of the parity symmetry. In some of the
phases long range forces emerge which may result in logarithmic confinement.
These include a dilaton exchange which plays a role also in the case when the
theory has no gauge symmetry. Gauged Lagrangian realizations of the 2D coset
models do not lead to emergent Maxwell terms. We discuss a case where the gauge
symmetry is anomalous.
