SciPost Submission Page
The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
by Cyril Closset, Horia Magureanu
Submission summary
| Authors (as registered SciPost users): | Cyril Closset · Horia Magureanu |
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| Preprint Link: | https://arxiv.org/abs/2107.03509v2 (pdf) |
| Date accepted: | Jan. 3, 2022 |
| Date submitted: | July 30, 2021, 10:24 a.m. |
| Submitted by: | Cyril Closset |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
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Abstract
The simplest non-trivial 5d superconformal field theories (SCFT) are the famous rank-one theories with $E_n$ flavour symmetry. We study their $U$-plane, which is the one-dimensional Coulomb branch of the theory on $\mathbb{R}^4 \times S^1$. The total space of the Seiberg-Witten (SW) geometry -- the $E_n$ SW curve fibered over the $U$-plane -- is described as a rational elliptic surface with a singular fiber of type $I_{9-n}$ at infinity. A classification of all possible Coulomb branch configurations, for the $E_n$ theories and their 4d descendants, is given by Persson's classification of rational elliptic surfaces. We show that the global form of the flavour symmetry group is encoded in the Mordell-Weil group of the SW elliptic fibration. We study in detail many special points in parameters space, such as points where the flavour symmetry enhances, and/or where Argyres-Douglas and Minahan-Nemeschansky theories appear. In a number of important instances, including in the massless limit, the $U$-plane is a modular curve, and we use modularity to investigate aspects of the low-energy physics, such as the spectrum of light particles at strong coupling and the associated BPS quivers. We also study the gravitational couplings on the $U$-plane, matching the infrared expectation for the couplings $A(U)$ and $B(U)$ to the UV computation using the Nekrasov partition function.
Published as SciPost Phys. 12, 065 (2022)
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2021-12-15 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2107.03509v2, delivered 2021-12-15, doi: 10.21468/SciPost.Report.4049
Report
This paper is exceptionally clearly-written. Also, it is nicely self-contained, as it includes very clear short reviews of the necessary background field theory, string theory constructions, and math.
Report #1 by Anonymous (Referee 1) on 2021-10-8 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2107.03509v2, delivered 2021-10-08, doi: 10.21468/SciPost.Report.3629
Strengths
1- Very well written, and clear. Excellent review and overview of the vast literature on the subject, including also the needed results from mathematics. The paper aims and succeeds in being relatively self-contained. The referencing is also very complete. 2-Contains interesting new results about the rank 1 5d SCFTs compactified on a circle to 4d, with clarifications and extensions of previous results from the literature. 3- Many interesting, useful interconnections with string theory and geometry are further explored, extending previous results from the literature. 4-Extensive, helpful discussion of the details in many special cases, including RG flow relations between theories.
Weaknesses
1- The strengths listed above unavoidably lead to a long paper, with the new results interspersed with the nice review. A rushed reader can find the highlights of the new results summarized in the excellent introduction.
Report
Requested changes
None.