## Rank $Q$ E-string on a torus with flux

Sara Pasquetti, Shlomo S. Razamat, Matteo Sacchi, Gabi Zafrir

SciPost Phys. 8, 014 (2020) · published 29 January 2020

- doi: 10.21468/SciPostPhys.8.1.014
- Submissions/Reports

### Abstract

We discuss compactifications of rank $Q$ E-string 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 S-duality 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.

### Cited by 2

### Ontology / Topics

See full Ontology or Topics database.### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1 }Sara Pasquetti, -
^{2 }Shlomo Razamat, -
^{1 }Matteo Sacchi, -
^{3 }Gabi Zafrir

^{1}Università degli Studi di Milano-Bicocca / University of Milano-Bicocca [UNIMIB]^{2}הטכניון – מכון טכנולוגי לישראל / Technion – Israel Institute of Technology^{3}東京大学 / University of Tokyo [UT]

- European Research Council [ERC]
- Instituto Nazionale di Fisica Nucleare (INFN) (through Organization: Istituto Nazionale di Fisica Nucleare / National Institute for Nuclear Physics [INFN])
- Israel Science Foundation [ISF]
- 文部科学省 Monbu-kagaku-shō / Ministry of Education, Culture, Sports, Science and Technology [MEXT]
- Università degli Studi di Milano-Bicocca / University of Milano-Bicocca [UNIMIB]