Effective field theory description of the higher dimensional quantum hall liquid

Bogdan Andrei Bernevig; Chyh Hong Chern; Jiang Ping Hu; Nicolaos Toumbas; Shou Cheng Zhang

doi:10.1006/aphy.2002.6292

Effective field theory description of the higher dimensional quantum hall liquid

Bogdan Andrei Bernevig
, Chyh Hong Chern
, Jiang Ping Hu
, Nicolaos Toumbas
, Shou Cheng Zhang

Research output: Contribution to journal › Article › peer-review

84 Scopus citations

Abstract

We derive an effective topological field theory model of the four dimensional quantum Hall liquid state recently constructed by Zhang and Hu. Using a generalization of the flux attachment transformation, the effective field theory can be formulated as a U(1) Chern-Simons theory over the total configuration space CP₃, or as a SU(2) Chern-Simons theory over S⁴. The new quantum Hall liquid supports various types of topological excitations, including the o-brane (particles), the 2-brane (membranes), and the 4-brane. There is a topological phase interaction among the membranes which generalizes the concept of fractional statistics.

Original language	English (US)
Pages (from-to)	185-207
Number of pages	23
Journal	Annals of Physics
Volume	300
Issue number	2
DOIs	https://doi.org/10.1006/aphy.2002.6292
State	Published - Sep 15 2002
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

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10.1006/aphy.2002.6292

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@article{1c950d654d4f4b8392b18a98a6866785,

title = "Effective field theory description of the higher dimensional quantum hall liquid",

abstract = "We derive an effective topological field theory model of the four dimensional quantum Hall liquid state recently constructed by Zhang and Hu. Using a generalization of the flux attachment transformation, the effective field theory can be formulated as a U(1) Chern-Simons theory over the total configuration space CP3, or as a SU(2) Chern-Simons theory over S4. The new quantum Hall liquid supports various types of topological excitations, including the o-brane (particles), the 2-brane (membranes), and the 4-brane. There is a topological phase interaction among the membranes which generalizes the concept of fractional statistics.",

author = "Bernevig, \{Bogdan Andrei\} and Chern, \{Chyh Hong\} and Hu, \{Jiang Ping\} and Nicolaos Toumbas and Zhang, \{Shou Cheng\}",

note = "Funding Information: We acknowledge useful discussions with M. Fabinger, D. Oprea, A. Polyakov, D. Santiago, L. Susskind, and F. Wilczek. N.T. thanks N. Arkani-Hamed, S. Minwalla, L. Motl, S. Nam, A. Neitzke, and B. Pioline. C.H.C. is grateful to W.-Y. Chuang for stimulating discussions. This work is supported by the NSF under Grant DMR-9814289. J.P. Hu is also supported by the Stanford Graduate fellowship. The work of N.T. is supported by the DOE, Grant DE-FG02-91ER40654.",

year = "2002",

month = sep,

day = "15",

doi = "10.1006/aphy.2002.6292",

language = "English (US)",

volume = "300",

pages = "185--207",

journal = "Annals of Physics",

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publisher = "Academic Press Inc.",

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TY - JOUR

T1 - Effective field theory description of the higher dimensional quantum hall liquid

AU - Bernevig, Bogdan Andrei

AU - Chern, Chyh Hong

AU - Hu, Jiang Ping

AU - Toumbas, Nicolaos

AU - Zhang, Shou Cheng

N1 - Funding Information: We acknowledge useful discussions with M. Fabinger, D. Oprea, A. Polyakov, D. Santiago, L. Susskind, and F. Wilczek. N.T. thanks N. Arkani-Hamed, S. Minwalla, L. Motl, S. Nam, A. Neitzke, and B. Pioline. C.H.C. is grateful to W.-Y. Chuang for stimulating discussions. This work is supported by the NSF under Grant DMR-9814289. J.P. Hu is also supported by the Stanford Graduate fellowship. The work of N.T. is supported by the DOE, Grant DE-FG02-91ER40654.

PY - 2002/9/15

Y1 - 2002/9/15

N2 - We derive an effective topological field theory model of the four dimensional quantum Hall liquid state recently constructed by Zhang and Hu. Using a generalization of the flux attachment transformation, the effective field theory can be formulated as a U(1) Chern-Simons theory over the total configuration space CP3, or as a SU(2) Chern-Simons theory over S4. The new quantum Hall liquid supports various types of topological excitations, including the o-brane (particles), the 2-brane (membranes), and the 4-brane. There is a topological phase interaction among the membranes which generalizes the concept of fractional statistics.

AB - We derive an effective topological field theory model of the four dimensional quantum Hall liquid state recently constructed by Zhang and Hu. Using a generalization of the flux attachment transformation, the effective field theory can be formulated as a U(1) Chern-Simons theory over the total configuration space CP3, or as a SU(2) Chern-Simons theory over S4. The new quantum Hall liquid supports various types of topological excitations, including the o-brane (particles), the 2-brane (membranes), and the 4-brane. There is a topological phase interaction among the membranes which generalizes the concept of fractional statistics.

UR - https://www.scopus.com/pages/publications/0037106605

UR - https://www.scopus.com/pages/publications/0037106605#tab=citedBy

U2 - 10.1006/aphy.2002.6292

DO - 10.1006/aphy.2002.6292

M3 - Article

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SN - 0003-4916

VL - 300

SP - 185

EP - 207

JO - Annals of Physics

JF - Annals of Physics

IS - 2

ER -

Effective field theory description of the higher dimensional quantum hall liquid

Abstract

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