SciPost Submission Page
Rank $Q$ EString on Spheres with Flux
by Chiung Hwang, Shlomo S. Razamat, Evyatar Sabag, Matteo Sacchi
Submission summary
As Contributors:  Chiung Hwang 
Preprint link:  scipost_202104_00009v1 
Date submitted:  20210408 10:24 
Submitted by:  Hwang, Chiung 
Submitted to:  SciPost Physics 
Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We consider compactifications of rank $Q$ Estring 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 WessZumino 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 Sconfinement 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 twosphere. 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.
Current status:
Submission & Refereeing History
You are currently on this page
Reports on this Submission
Anonymous Report 1 on 202159 Invited Report
Strengths
1  provides a new construction of a class of theories that opens up potential new vantage points on certain symmetries and features
2  concrete checks of the proposed construction via detailed computation of anomalies
3  clarity of the presentation, well written
Weaknesses
1  it might be useful to add a more concrete discussion on how these results can be used for future computations and new directions
Report
In this paper the authors construct compactifications of the rank $Q$ Estring theory on a sphere with different amounts of flux. These theories can be obtained from a 6dimensional $\mathcal{N}=(1,0)$ SCFT that is realised by $Q$ M5branes probing an M9brane. In this paper the authors present a different construction by gluing together different theories on punctured spheres with specific flux: indeed, starting from the socalled tube model (a theory on a twopunctured sphere) considered previously in the literature (by some of the current authors), the authors create the socalled cap model by 'closing' one of the punctures by introducing suitable vevs and adding gauge invariant flipping fields to obtain the correct anomalies. Compactifications of the Estring theories can be obtained by gluing cap and tube models via adding chiral fields in a suitable representation of various $Usp(2Q)$ symmetries appearing in the tube models. The authors analyse the symmetry content of the resulting theories and calculate the anomalies to check whether they indeed correspond to the rank $Q$ Estring theories.
As far as I can tell, the computations in this paper are genuine and lead to interesting and novel results: they lead to a new construction of a class of interesting theories that gives a new angle on certain of its properties and symmetries, for example a geometric interpretation of the appearance of an $E_6$ symmetry in a sphere model that was previously discussed in the literature. Furthermore, the paper is well structured and the various appendices make it fairly accessible. Based on this, I recommend it for publication.
There are only very few minor points that perhaps the authors could comment on:
) it would be helpful to discuss in the main text some of the notation that is used throughout. While there is appendix D, it might help, for example to clarify in eq.(3) which chemical potentials $p$ and $q$ encode
) after eq.(12): it would be very helpful to elaborate to what degree checking that the two models have the same anomalies guarantees that indeed the theory constructed here is a compactification of the Estring theory, or (if so) which possible ambiguities are left
) eq.(19): comparing with eq.(12), I don't understand why the argument of the $\Gamma_e$ in the first product contains $x_n$ rather than $y_n$
) I don't understand how the numerical value of $R_b$ in eq.(63) has been obtained (or similar results in subsequent sections)
) When gluing various cap and tube theories together by adding chiral fields, are there any constraints on the choice of $\Phi$ or $S$gluing? While I understand that in order to reproduce the correct Estring models, a particular choice is required, is it clear that other choices lead to inherently inconsistent models or are there a priori also other viable theories? Does this for example produce inconsistencies at the level of the obtained anomalies, thus providing intrinsic selection rules?
) The authors have not included a Conclusion section: I agree with their decision that they have (notably in the Introduction) outlined their results and put them into context (such that a Conclusion would be a repetition of what has been already said). However, an aspect which might be interesting to discuss is what other possibilities the description of the Estring theories in the current theory entails: since the tube theory is well studied (and runs to a simple WZW model), does this allow other quantities (i.e. other than anomalies) to be computed which are inaccessible by other methods? Can the current methods be applied to other classes of compactifications?