(1,0) gauge theories on the six-sphere

Naseer, Usman

doi:10.21468/SciPostPhys.6.1.002

SciPost Physics

(1,0) gauge theories on the six-sphere

Usman Naseer

SciPost Phys. 6, 002 (2019) · published 8 January 2019

doi: 10.21468/SciPostPhys.6.1.002
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Abstract

We construct gauge theories with a vector-multiplet and hypermultiplets of $(1,0)$ supersymmetry on the six-sphere. The gauge coupling on the sphere depends on the polar angle. This has a natural explanation in terms of the tensor branch of $(1,0)$ theories on the six-sphere. For the vector-multiplet we give an off-shell formulation for all supersymmetries. For hypermultiplets we give an off-shell formulation for one supersymmetry. We show that the path integral for the vector-multiplet localizes to solutions of the Hermitian-Yang-Mills equation, which is a generalization of the (anti-)self duality condition to higher dimensions. For the hypermultiplet, the path integral localizes to configurations where the field strengths of two complex scalars are related by an almost complex structure.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.6.1.002
TI  - (1,0) gauge theories on the six-sphere
PY  - 2019/01/08
UR  - https://www.scipost.org/SciPostPhys.6.1.002
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 6
IS  - 1
SP  - 002
A1  - Naseer, Usman
AB  - We construct gauge theories with a vector-multiplet and hypermultiplets of $(1,0)$ supersymmetry on the six-sphere. The gauge coupling on the sphere depends on the polar angle. This has a natural explanation in terms of the tensor branch of $(1,0)$ theories on the six-sphere. For the vector-multiplet we give an off-shell formulation for all supersymmetries. For hypermultiplets we give an off-shell formulation for one supersymmetry. We show that the path integral for the vector-multiplet localizes to solutions of the Hermitian-Yang-Mills equation, which is a generalization of the (anti-)self duality condition to higher dimensions. For the hypermultiplet, the path integral localizes to configurations where the field strengths of two complex scalars are related by an almost complex structure.
ER  -

@Article{10.21468/SciPostPhys.6.1.002,
	title={{(1,0) gauge theories on the six-sphere}},
	author={Usman Naseer},
	journal={SciPost Phys.},
	volume={6},
	pages={002},
	year={2019},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.6.1.002},
	url={https://scipost.org/10.21468/SciPostPhys.6.1.002},
}

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Gauge theory Supersymmetry

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¹ ² Usman Naseer

Funders for the research work leading to this publication

Knut och Alice Wallenbergs Stiftelse (Knut and Alice Wallenberg Foundation) (through Organization: Knut och Alice Wallenbergs Stiftelse / Knut and Alice Wallenberg Foundation)
United States Department of Energy [DOE]