SciPost Submission Page
Rank $Q$ Estring on a torus with flux
by Sara Pasquetti, Shlomo S. Razamat, Matteo Sacchi, Gabi Zafrir
This Submission thread is now published as
Submission summary
Authors (as Contributors):  Sara Pasquetti · Shlomo Razamat · Matteo Sacchi 
Submission information  

Arxiv Link:  https://arxiv.org/abs/1908.03278v2 (pdf) 
Date accepted:  20200122 
Date submitted:  20200115 01:00 
Submitted by:  Razamat, Shlomo 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We discuss compactifications of rank $Q$ Estring theory on a torus with fluxes for abelian subgroups of the $E_8$ global symmetry of the $6d$ SCFT. We argue that the theories corresponding to such tori are built from a simple model we denote as $E[USp(2Q)]$. This model has a variety of non trivial properties. In particular the global symmetry is $USp(2Q)\times USp(2Q)\times U(1)^2$ with one of the two $USp(2Q)$ symmetries emerging in the IR as an enhancement of an $SU(2)^Q$ symmetry of the UV Lagrangian. The $E[USp(2Q)]$ model after dimensional reduction to $3d$ and a subsequent Coulomb branch flow is closely related to the familiar $3d$ $T[SU(Q)]$ theory, the model residing on an Sduality domain wall of $4d$ $\mathcal{N}=4$ $SU(Q)$ SYM. Gluing the $E[USp(2Q)]$ models by gauging the $USp(2Q)$ symmetries with proper admixtures of chiral superfields gives rise to systematic constructions of many examples of $4d$ theories with emergent IR symmetries. We support our claims by various checks involving computations of anomalies and supersymmetric partition functions. Many of the needed identities satisfied by the supersymmetric indices follow directly from recent mathematical results obtained by E. Rains.
Published as SciPost Phys. 8, 014 (2020)
Author comments upon resubmission
List of changes
Referee I:
1  We have rechecked the equation 4.18 and it is OK as written. (One issue that often causes mistakes is that the antisymmetric fields should be remembered to be taken traceless.)
2  We have added footnote 1 on page 4 to comment on the needed holonomy.
3  We have added the reference to fields $b_n$ in the caption of Figure 3.
4  We added footnote 8 to refer to equation 3.19 for the proper relation between the parameters.
We have fixed the typos found by the referee.
Referee II:
1  We fixed equation 2.5. We thank the referee for spotting this typo.
2  We streamlined the references to different types of models. In particular we now refer only to $FM[SU(Q)]$ and not to $FM[U(Q)]$. The partition function of FM[U(Q)] appears only in intermediate steps of the calculation and we added a comment around 5.24 to explain how it is related to the one of $FM[SU(Q)]$.
4  We added a comment below 3.13 explaining how the entry should be determined.
6  We have rephrased the discussion around equation 5.2.
We have fixed the typos and parsing issues mentioned by the referee.