From D = 3 to D = 2 dimensions: A note on topological order

Abstract

We construct, by a procedure involving a dimensional reduction from a ChernSimons theory with borders, an effective theory for 1 + 1 dimensional superconductor. That system can be either in an ordinary phase or in a topological one, depending on the value of two phases, corresponding to complex order parameters. Finally, we argue that the original theory and its dimensionally reduced one can be related to the effective action for a quantum Dirac field in a slab geometry, coupled to a gauge field.