Index theorem for topological excitations on R^3 * S^1 and Chern-Simons theory

Understand

We derive an index theorem for the Dirac operator in the background of various topological excitations on an R^3 \times S^1 geometry.

• The index theorem provides more refined data than the APS index for an instanton on R^4 and reproduces it in decompactification limit.
• In the R^3 limit, it reduces to the Callias index theorem.
• The index is expressed in terms of topological charge and the eta-invariant associated with the boundary Dirac operator.