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Dualities and loops on squashed $S^3$

by Charles Thull

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Submission summary

Authors (as registered SciPost users): Charles Thull
Submission information
Preprint Link:  (pdf)
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Date accepted: 2023-09-12
Date submitted: 2023-08-07 08:57
Submitted by: Thull, Charles
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory


We consider $\mathcal{N}=4$ supersymmetric gauge theories on the squashed three-sphere with six preserved supercharges. We first discuss how Wilson and vortex loops preserve up to four of the supercharges and we find squashing independence for the expectation values of these $\frac{2}{3}$-BPS loops. We then show how the additional supersymmetries facilitate the analytic matching of partition functions and loop operator expectation values to those in the mirror dual theory, allowing one to lift all the results that were previously established on the round sphere to the squashed sphere. Additionally, on the squashed sphere with four preserved supercharges, we numerically evaluate the partition functions of ABJM and its dual super-Yang-Mills at low ranks of the gauge group. We find matching values of their partition functions, prompting us to conjecture the general equality on the squashed sphere. From the numerics we also observe the squashing dependence of the Lee-Yang zeros and of the non-perturbative corrections to the all order large $N$ expression for the ABJM partition function.

Published as SciPost Phys. 15, 156 (2023)

Author comments upon resubmission

We thank the referees for their careful reading of the manuscript. We have included all of their suggestions in the new manuscript, a list of changes is given.

List of changes

1. Fixed figures 2(b) and 3(b) to show annotation of vertical axes
2. Fixed several typos
3. Made language on supersymmetry of backgrounds and gauge theories clearer throughout the whole manuscript: To the backgrounds we now refer only by the number of supercharges they preserve. To the gauge theories we refer by the amount of supersymmetry they have in flat space. Added a footnote in the introduction to clarify this point. This has affected in section 1 paragraphs 2, 3, 6, 9, in section 2 paragraph 1 as well as after equation (2.7) and before (2.11), in section 3 the paragraphs after equations (3.5) and (3.6) and in section 4.1 the ends of paragraphs 1, 2 and 3.
4. Added a clarification on the fields in the defining equation (3.1) for the Wilson loop
5. Added a clarification for the notation in the second line of equation (4.4)
6. In section 4, made it more explicit that we are discussing the duality mapping at the level of partition functions and loop operators. The main changes are the first paragraph of the section as well as the captions to Figures 6 and 8
7. Added a paragraph in subsection 4.2 on expected numerical errors
8. Added comparison to the exact round sphere result on the full mass and FI parameter range with two additional figures
9. In all of subsection 4.2, changed wordings to reflect the comparison to the expected errors

Reports on this Submission

Anonymous Report 2 on 2023-9-4 (Invited Report)


The revision addresses the requested changes and I therefore recommend publication.

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Anonymous Report 1 on 2023-8-25 (Invited Report)


The author has made appropriate changes. I would like to recommend the manuscript for publication.

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