We compute the finite temperature induced fermion number for fermions coupled to a static nonlinear sigma model background in $2+1$ dimensions, in the derivative expansion limit. While the zero temperature induced fermion number is well known to be topological (it is the winding number of the background), at finite temperature there is a temperature dependent correction that is nontopological—this finite T correction is sensitive to the detailed shape of the background. At low temperature we resum the derivative expansion to all orders, and we consider explicit forms of the background as a $\mathcal{C}{\mathcal{P}}^1$ instanton or as a baby Skyrmion.

• Received 9 April 2002

DOI:https://doi.org/10.1103/PhysRevD.66.025004