On Some Special Cases of Gaiotto's Positivity Conjecture

Pavel Etingof

Department of Mathematics, MIT, Cambridge, MA 02139, USA

Abstract: We prove a conjecture of D. Gaiotto on positivity of inner products arising in studying Landau–Ginzburg boundary conditions in the 1-dimensional case, and in special cases in higher dimensions, for 3d free hypermultiplets.

Keywords: gauge theory, total positivity, positive definite function, Bochner's theorem.

MSC: 81T13, 42A82, 15B48

Received: February 29, 2024; in final form July 11, 2024; Published online July 13, 2024

Language: English

DOI: 10.3842/SIGMA.2024.063

ArXiv: 2402.17174