V. Lysov

A new proof of the Chern–Gauss–Bonnet theorem is derived using supersymmetry and BV localisation, reducing geometry to critical points.

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.

Chern-Gauss-Bonnet theorem via BV localization