Schwinger’s Closed Time Path formalism is the basis of modern treatments of cosmological field theories, hydrodynamics and open quantum systems. Its application to gauge theories at finite temperature is well studied, relying on KMS boundary conditions and complex-time contours. By contrast the discussion of gauge theories such as Yang-Mills out of equilibrium has been less well developed, in large part due to a lack of development of how to treat gauge issues and Faddeev-Popov-DeWitt ghosts on the CTP. I will show how to construct the CTP in the BRST formalism, where a single diagonal copy of BRST symmetry survives, and how to implement the boundary conditions for ghosts for arbitrary initial physical states. As an illustration I will discuss how Hard-thermal-loop EFTs can be viewed as open quantum systems, and how to construct an open EFT for a gauge theory in a Higgs phase. 

An anomaly for a global symmetry G says “no”. It stops us from driving the theory to a trivially gapped phase while preserving G. Relatedly, it also prevents us from constructing boundary conditions that preserve G, without adding additional boundary degrees of freedom.

Does a vanishing anomaly say “yes”? It has been proposed that both of these statements can be upgraded to “if and only if” statements. We probe both of these proposals in the simplest theory in which they are non-trivial: the theory of two Dirac fermions in two dimensions, with G chiral. 

Along the way, we will construct all self-duality defects of two free Weyl fermions that arise from gauging an invertible symmetry. These play a central role then in the construction of symmetric boundaries for two Dirac fermions.