## Rank $Q$ E-string on spheres with flux

Chiung Hwang, Shlomo S. Razamat, Evyatar Sabag, Matteo Sacchi

SciPost Phys. 11, 044 (2021) · published 30 August 2021

- doi: 10.21468/SciPostPhys.11.2.044
- Submissions/Reports

### 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.

### Cited by 18

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}Chiung Hwang, -
^{2}^{3}Shlomo S. Razamat, -
^{3}Evyatar Sabag, -
^{4}Matteo Sacchi

^{1}University of Cambridge^{2}Princeton University^{3}הטכניון – מכון טכנולוגי לישראל / Technion – Israel Institute of Technology^{4}Università degli Studi di Milano-Bicocca / University of Milano-Bicocca [UNIMIB]

- European Research Council [ERC]
- German-Israeli Foundation for Scientific Research and Development [GIF]
- Institute for Advanced Study (IAS) (through Organization: Institute for Advanced Study, Princeton [IAS])
- Israel Science Foundation [ISF]
- Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR) (through Organization: Ministero dell'Istruzione, dell'Università e della Ricerca / Ministry of Education, Universities and Research [MIUR])
- Science and Technology Facilities Council [STFC]
- United States - Israel Binational Science Foundation (through Organization: United States-Israel Binational Science Foundation [BSF])
- Università degli Studi di Milano-Bicocca / University of Milano-Bicocca [UNIMIB]