1. When the Fourier transform is one loop exact?
- Author
-
Kontsevich, Maxim and Odesskii, Alexander
- Subjects
Mathematics - Algebraic Geometry ,High Energy Physics - Theory ,Mathematical Physics - Abstract
We investigate the question: for which functions $f(x_1,...,x_n),~g(x_1,...,x_n)$ the asymptotic expansion of the integral $\int g(x_1,...,x_n) e^{\frac{f(x_1,...,x_n)+x_1y_1+...+x_ny_n}{\hbar}}dx_1...dx_n$ consists only of the first term. We reveal a hidden projective invariance of the problem which establishes its relation with geometry of projective hypersurfaces of the form $\{(1:x_1:...:x_n:f)\}$. We also construct various examples, in particular we prove that Kummer surface in $\mathbb{P}^3$ gives a solution to our problem., Comment: 53 pages
- Published
- 2023