### Abstract

We present a 6D generalization of the fractional quantum Hall effect involving membranes coupled to a three-form potential in the presence of a large background four-form flux. The low energy physics is governed by a bulk 7D topological field theory of abelian three-form potentials with a single derivative Chern-Simons-like action coupled to a 6D anti-chiral theory of Euclidean effective strings. We derive the fractional conductivity, and explain how continued fractions which figure prominently in the classification of 6D superconformal field theories correspond to a hierarchy of excited states. Using methods from conformal field theory we also compute the analog of the Laughlin wavefunction. Compactification of the 7D theory provides a uniform perspective on various lower-dimensional gapped systems coupled to boundary degrees of freedom. We also show that a supersymmetric version of the 7D theory embeds in M-theory, and can be decoupled from gravity. Encouraged by this, we present a conjecture in which IIB string theory is an edge mode of a 10 + 2-dimensional bulk topological theory, thus placing all twelve dimensions of F-theory on a physical footing.

Language | English (US) |
---|---|

Article number | 120 |

Journal | Journal of High Energy Physics |

Volume | 2018 |

Issue number | 5 |

DOIs | |

State | Published - May 1 2018 |

### Fingerprint

### Keywords

- Chern-Simons Theories
- M-Theory
- Topological Field Theories
- Topological States of Matter

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2018*(5), [120]. https://doi.org/10.1007/JHEP05(2018)120

**6D fractional quantum Hall effect.** / Heckman, Jonathan J.; Tizzano, Luigi.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2018, no. 5, 120. https://doi.org/10.1007/JHEP05(2018)120

}

TY - JOUR

T1 - 6D fractional quantum Hall effect

AU - Heckman, Jonathan J.

AU - Tizzano, Luigi

PY - 2018/5/1

Y1 - 2018/5/1

N2 - We present a 6D generalization of the fractional quantum Hall effect involving membranes coupled to a three-form potential in the presence of a large background four-form flux. The low energy physics is governed by a bulk 7D topological field theory of abelian three-form potentials with a single derivative Chern-Simons-like action coupled to a 6D anti-chiral theory of Euclidean effective strings. We derive the fractional conductivity, and explain how continued fractions which figure prominently in the classification of 6D superconformal field theories correspond to a hierarchy of excited states. Using methods from conformal field theory we also compute the analog of the Laughlin wavefunction. Compactification of the 7D theory provides a uniform perspective on various lower-dimensional gapped systems coupled to boundary degrees of freedom. We also show that a supersymmetric version of the 7D theory embeds in M-theory, and can be decoupled from gravity. Encouraged by this, we present a conjecture in which IIB string theory is an edge mode of a 10 + 2-dimensional bulk topological theory, thus placing all twelve dimensions of F-theory on a physical footing.

AB - We present a 6D generalization of the fractional quantum Hall effect involving membranes coupled to a three-form potential in the presence of a large background four-form flux. The low energy physics is governed by a bulk 7D topological field theory of abelian three-form potentials with a single derivative Chern-Simons-like action coupled to a 6D anti-chiral theory of Euclidean effective strings. We derive the fractional conductivity, and explain how continued fractions which figure prominently in the classification of 6D superconformal field theories correspond to a hierarchy of excited states. Using methods from conformal field theory we also compute the analog of the Laughlin wavefunction. Compactification of the 7D theory provides a uniform perspective on various lower-dimensional gapped systems coupled to boundary degrees of freedom. We also show that a supersymmetric version of the 7D theory embeds in M-theory, and can be decoupled from gravity. Encouraged by this, we present a conjecture in which IIB string theory is an edge mode of a 10 + 2-dimensional bulk topological theory, thus placing all twelve dimensions of F-theory on a physical footing.

KW - Chern-Simons Theories

KW - M-Theory

KW - Topological Field Theories

KW - Topological States of Matter

UR - http://www.scopus.com/inward/record.url?scp=85047550829&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047550829&partnerID=8YFLogxK

U2 - 10.1007/JHEP05(2018)120

DO - 10.1007/JHEP05(2018)120

M3 - Article

VL - 2018

JO - Journal of High Energy Physics

T2 - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 5

M1 - 120

ER -