## SciPost Submission Page

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

### by Usman Naseer

####
- Published as
SciPost Phys.
**6**,
2
(2019)

### Submission summary

As Contributors: | Usman Naseer |

Arxiv Link: | https://arxiv.org/abs/1809.06272v3 |

Date accepted: | 2018-12-19 |

Date submitted: | 2018-12-04 |

Submitted by: | Naseer, Usman |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | High-Energy Physics - Theory |

### 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.

###### Current status:

**6**, 2 (2019)

### Ontology / Topics

See full Ontology or Topics database.### Author comments upon resubmission

Dear Editor,

In this revised version I have fixed several typos pointed out by all three referees. An important change is the discussion about the regularity of the vector-multiplet action at the end of section 3. This point was raised by two referees.

Thank you,

-Usman

### List of changes

1. "vector-multiplet" changed to "vector multiplet" in a lot of places.

2. end of intro: "furhter"->"further"

3. in sec.2, new reference is added [arXiv:1209.5408], which also discussed 4d N=1 susy on S^4.

4.before eq.(4.6): "cupling"-->"coupling"

5.after eq.(4.12): "in above arguments"-->"in the above argument"

6.intro to sec.5: "except the south pole"-->"except at the south pole"

7.before eq.(5.3): "contirbute"-->"contribute"

8.middle of sec.6: "be achieve by"-->"be achieved by"

9.end of sec.6: "à la localization" with "à".

10. Typo in eq. 5.9 is fixed.

11. At the end of section 3, a field redefinition is discussed which makes the Lagrangian manifestly regular everywhere.

12. chirality condition is explicitly mentioned in the beginning of section 2 after 2.2

### Submission & Refereeing History

- Report 2 submitted on 2018-12-05 11:39 by
*Anonymous* - Report 1 submitted on 2018-12-05 11:22 by Dr Assel

## Reports on this Submission

### Anonymous Report 2 on 2018-12-5 Invited Report

### Strengths

See previous version.

### Weaknesses

See previous version.

### Report

This is an interesting and topical paper. See my review of the previous version. The new version has only minor changes. This is a good paper that I would recommend for publication.

### Requested changes

none.

### Report 1 by Benjamin Assel on 2018-12-5 Invited Report

### Report

The modifications address the minor issues raised in the previous report.