Witten-Reshetikhin-Turaev invariants and homological blocks for plumbed homology spheres

Autor:	Murakami, Yuya
Rok vydání:	2022
Předmět:	Mathematics - Geometric Topology High Energy Physics - Theory Mathematical Physics Mathematics - Number Theory Mathematics - Quantum Algebra 57K31 57K10 57K16 11F27 11L05 11T24
Druh dokumentu:	Working Paper
Popis:	In this paper, we prove a conjecture by Gukov-Pei-Putrov-Vafa for a wide class of plumbed 3-manifolds. Their conjecture states that Witten-Reshetikhin-Turaev (WRT) invariants are radial limits of homological blocks, which are $ q $-series introduced by them for plumbed 3-manifolds with negative definite linking matrices. The most difficult point in our proof is to prove the vanishing of weighted Gauss sums that appear in coefficients of negative degree in asymptotic expansions of homological blocks. To deal with it, we develop a new technique for asymptotic expansions, which enables us to compare asymptotic expansions of rational functions and false theta functions related to WRT invariants and homological blocks, respectively. In our technique, our vanishing results follow from holomorphy of such rational functions. Comment: 18 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2205.01282 Zobrazit plný text záznamu View this record from Arxiv