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Rank $Q$ E-String on Spheres with Flux
by Chiung Hwang, Shlomo S. Razamat, Evyatar Sabag, Matteo Sacchi
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Chiung Hwang · Shlomo Razamat |
| Submission information | |
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| Preprint Link: | scipost_202104_00009v2 (pdf) |
| Date accepted: | 2021-08-20 |
| Date submitted: | 2021-07-27 18:25 |
| Submitted by: | Hwang, Chiung |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We consider compactifications of rank $Q$ E-string theory on a genus zero surface with no punctures but with flux for various subgroups of the $\mathrm{E}_8\times \mathrm{SU}(2)$ global symmetry group of the six dimensional theory. We first construct a simple Wess--Zumino model in four dimensions corresponding to the compactification on a sphere with one puncture and a particular value of flux, the cap model. Using this theory and theories corresponding to two punctured spheres with flux, one can obtain a large number of models corresponding to spheres with a variety of fluxes. These models exhibit interesting IR enhancements of global symmetry as well as duality properties. As an example we will show that constructing sphere models associated to specific fluxes related by an action of the Weyl group of $\mathrm{E}_8$ leads to the S-confinement duality of the $\mathrm{USp}(2Q)$ gauge theory with six fundamentals and a traceless antisymmetric field. Finally, we show that the theories we discuss possess an $\mathrm{SU}(2)_{\text{ISO}}$ symmetry in four dimensions that can be naturally identified with the isometry of the two-sphere. We give evidence in favor of this identification by computing the `t Hooft anomalies of the $\mathrm{SU}(2)_{\text{ISO}}$ in 4d and comparing them with the predicted anomalies from 6d.
Author comments upon resubmission
List of changes
Report I:
1. We have added the definition of the superconformal index in eq. (3) with a brief explanation of the notation after that.
2. We have commented in the paragraph after eq. (14) on the evidence we provide to support our cap model, which is supposed to flow to the same IR fixed point as the E-string theory compactified on a sphere with a puncture.
3. We have corrected the typos the referee pointed out.
4. $R_b$ in eq. (65), which was (63) in the previous version, is obtained by the a-maximization as we explained in the paragraph before eq. (64).
5. We have added footnote 14 explaining the gluing should be taken in such a way that the resulting theory is anomaly-free.
6. We have added discussions for the possible extension of our result in the last paragraph of introduction.
Report II:
1. We have corrected the typos the referee pointed out.
2. We have briefly commented after eq. (66) why the rational approximation of the mixing coefficients is used in our analysis.
3. We have added an explanation for the quantization of the flux in footnote 5, which was footnote 4 in the previous version.
We have also fixed the typos in eqs. (6-7) because we missed $i \sigma_2$ in (6) and the vev $\mathsf{J}_Q$ in (7) is for $\mathsf{H}$ instead of $\mathsf{O_H}$, which is the flip field of $\mathsf{H}$. We have added eq. (5) to elaborate the explanation accordingly.
Published as SciPost Phys. 11, 044 (2021)