When the Fourier transform is one loop exact?

Maxim Kontsevich, Alexander Odesskii

We investigate the question: for which functions $f(x_1,...,x_n),g(x_1,...,x_n)$ the asymptotic expansion of the integral $\int g(x_1,...,x_n) e^{\frac{f(x_1,...,x_n)+x_1y_1+...+x…