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We study novel type of contributions to the partition function of the Maxwellsystem defined on a small compact manifold such as torus. These new terms cannot be described in terms of the physical propagating photons with twotransverse polarizations. Rather, these novel contributions emerge as a resultof tunnelling events when transitions occur between topologically different butphysically identical vacuum winding states. These new terms give an extracontribution to the Casimir pressure. The infrared physics in the system can bedescribed in terms of the topological auxiliary non-propagating fields$a_i(\mathbf{k})$ governed by Chern-Simons -like action. The system can bestudied in terms of these auxiliary fields precisely in the same way as atopological insulator can be analyzed in terms of Berry's connection${\cal{A}}_i(\mathbf{k})$. We also argue that the Maxwell vacuum defined on asmall 4-torus behaves very much in the same way as a topological insulator with$\theta\neq 0$.

Topological order and Berry connection for the Maxwell Vacuum on a four-torus