scholarly journals Odd primary homotopy types of the gauge groups of exceptional Lie groups

2019 ◽  
Vol 147 (4) ◽  
pp. 1751-1762 ◽  
Author(s):  
Sho Hasui ◽  
Daisuke Kishimoto ◽  
Tseleung So ◽  
Stephen Theriault
Keyword(s):  
Lie Groups ◽  
Gauge Groups ◽  
Homotopy Types ◽  
Exceptional Lie Groups

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

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Zhihao Duan ◽  
Kimyeong Lee ◽  
June Nahmgoong ◽  
Xin Wang
Keyword(s):  
Lie Groups ◽  
Point Of View ◽  
Partition Functions ◽  
Congruence Subgroups ◽  
Gauge Groups ◽  
Simple Lie Groups ◽  
Instanton Contribution ◽  
Elliptic Genera ◽  
Supersymmetric Gauge ◽  
The One

Abstract We study twisted circle compactification of 6d (2, 0) SCFTs to 5d $$ \mathcal{N} $$ 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 Γ0(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.

scholarly journals Samelson products in p-regular exceptional Lie groups

2014 ◽  
Vol 178 ◽  
pp. 17-29 ◽  
Author(s):  
Sho Hasui ◽  
Daisuke Kishimoto ◽  
Akihiro Ohsita
Keyword(s):  
Lie Groups ◽  
Exceptional Lie Groups

Geometries of Exceptional Lie Groups. Metasymplectic Geometries

1997 ◽  
pp. 331-369 ◽  
Author(s):  
Boris Rosenfeld
Keyword(s):  
Lie Groups ◽  
Exceptional Lie Groups

scholarly journals Random matrix theory, the exceptional Lie groups andL-functions

2003 ◽  
Vol 36 (12) ◽  
pp. 2933-2944 ◽  
Author(s):  
J P Keating ◽  
N Linden ◽  
Z Rudnick
Keyword(s):  
Lie Groups ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Exceptional Lie Groups

N > 2-extended Supergravity, U-duality and the Orbits of Exceptional Lie Groups

2006 ◽  
pp. 175-202
Author(s):  
Stefano Bellucci ◽  
Alessio Marrani ◽  
Sergio Ferrara
Keyword(s):  
Lie Groups ◽  
Exceptional Lie Groups

scholarly journals The Homotopy Types of Sp(2)-Gauge Groups over Closed Simply Connected Four-Manifolds

2019 ◽  
Vol 305 (1) ◽  
pp. 287-304
Author(s):  
Tseleung So ◽  
Stephen Theriault
Keyword(s):  
Gauge Groups ◽  
Homotopy Types ◽  
Four Manifolds ◽  
Simply Connected

Sheets and rigid orbit covers of exceptional Lie groups

1998 ◽  
Vol 43 (20) ◽  
pp. 1702-1707 ◽  
Author(s):  
Ke Liang ◽  
Linyuan Lu
Keyword(s):  
Lie Groups ◽  
Exceptional Lie Groups
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