Twisted 6d (2, 0) SCFTs on a circle

• Published in: The journal of high energy physics 2021-07, Vol.2021 (7), p.1-71, Article 179
• Main Authors: Duan, Zhihao, Lee, Kimyeong, Nahmgoong, June, Wang, Xin
• Format: Article
• Language: English
• Subjects: Brane Dynamics in Gauge Theories; Classical and Quantum Gravitation; Elementary Particles; F-Theory; Field Theories in Higher Dimensions; Gauge theory; High energy physics; Instantons; Invariants; Lie groups; Partitions (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Subgroups; Supersymmetric Gauge Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2021)179

A bstract We study twisted circle compactification of 6d (2 , 0) SCFTs to 5d N = 2 supersymmetric gauge theories with non-simply-laced gauge groups. We provide two complementary approaches towards the BPS partition functions, reflecting the 5d and 6d point of view respectively. The first is based on the blowup equations for the instanton partition function, from which in particular we determine explicitly the one-instanton contribution for all simple Lie groups. The second is based on the modular bootstrap program, and we propose a novel modular ansatz for the twisted elliptic genera that transform under the congruence subgroups Γ 0 ( N ) of SL(2 , ℤ). We conjecture a vanishing bound for the refined Gopakumar-Vafa invariants of the genus one fibered Calabi-Yau threefolds, upon which one can determine the twisted elliptic genera recursively. We use our results to obtain the 6d Cardy formulas and find universal behaviour for all simple Lie groups. In addition, the Cardy formulas remain invariant under the twist once the normalization of the compact circle is taken into account.