  We present a new proof for the Chern-Gauss-Bonnet theorem. We represent the
Euler class integral as the partition function for zero-dimensional field
theory with on-shell supersymmetry. We rewrite the supersymmetric partition
function as a BV integral and deform the Lagrangian submanifold. The new
Lagrangian submanifold localizes the BV integral to the critical points of the
Morse function.
