In chapter 4.3 of Gauge Fields and Strings Polyakov study effect of monopoles. He make few statements:
In 4d Maxwell theory with monopoles, exist phase transition, if $e_0^2> e_c^2$ it is confinement phase, if $e_0^2 < e_c^2$ is photonic phase.(See this question, I don't understand now physical essence of this transition).
In theory of 2-form gauge fields, one have confinement for all values of charges and situation is fully analogue to confinement in 3d Maxwell theory.
Presence of monopoles is essential detail in 1st statement, and as I understand, to save monopoles in continuous limit, one need consider this abelian theory as low-energy subsector of some non-abelian theory, for example Georgi-Glashow model. But it is not quite clear, because when one calculate path integral, one include monopole configuration to partition function. So, why we can't have phase transition in pure Maxwell theory?
About 2-form gauge fields is not clear much more. As I understand, in continuum limit we will have something like this: $$ S =\int d^4x \partial_{[\mu} A_{\nu\rho]} \partial^{[\mu} A^{\nu\rho]} $$ With equation of motion : $$ \partial_\mu\partial^{[\mu} A^{\nu\rho]} =0 $$
What is known about solutions of such equation?
What is monopole like object in such 2-form gauge theory?
Also, isn't clear for which non-abelian 2-form theory this theory may be low-energy theory. Polyakov wrote, that there's some problems for construction of such theories. I asked this question in this post.
