How Bob Laughlin Tamed the Giant Graviton from Taub-NUT Space

Brodie, John H.

doi:10.2172/784958

Cited by 26 publications

(48 citation statements)

References 19 publications

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“…Noncommutative geometry could also arise in matrix models [11,12] as a classical solution [13,14], [15,16]. Myers effects [17] could introduce additional terms to the matrix model and lead to new solutions [18][19][20]. We note that all these quantized geometries are characterized by a commutator and could be referred to as of Lie-algebra type.…”

Section: Introductionmentioning

confidence: 99%

D1-strings in large RR 3-form flux, quantum Nambu geometry and M5-branes in theC-field

Chu

Sehmbi

2012

J. Phys. A: Math. Theor.

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We consider D1-branes in a RR flux background and show that there is a low energy -large flux double scaling limit where the D1-branes action is dominated by a Chern-Simons-Myers coupling term. As a classical solution to the matrix model, we find a novel quantized geometry characterized by a quantum Nambu 3-bracket. Infinite dimensional representations of the quantum Nambu geometry are constructed which demonstrate that the quantum Nambu geometry is intrinsically different from the ordinary Lie algebra type noncommutative geometry. Matrix models for the IIB string, IIA string and M-theory in the corresponding backgrounds are constructed. A classical solution of a quantum Nambu geometry in the IIA Matrix string theory gives rise to an expansion of the fundamental strings into a system of multiple D4-branes and the fluctuation is found to describe an action for a non-abelian 3-form field strength which is a natural non-abelian generalization of the PST action for a single D4-brane. In view of the recent proposals [1, 2] of the M5-branes theory in terms of the D4-branes, we suggest a natural way to include all the KK modes and propose an action for the the multiple M5-branes in a constant C-field. The worldvolume of the M5-branes in a C-field is found to be described by a quantum Nambu geometry with self-dual parameters. It is intriguing that our action is naturally formulated in terms of a 1-form gauge field living on a six dimensional quantum Nambu geometry.

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Section: Introductionmentioning

confidence: 99%

D1-strings in large RR 3-form flux, quantum Nambu geometry and M5-branes in theC-field

Chu

Sehmbi

2012

J. Phys. A: Math. Theor.

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“…The rotating BEC is related to the QH effect for fermions, both integral and fractional, at small boson filling fractions [31]. Previously a possible realization of the QHE in string theory has been proposed in the literature [40], which involved particular configurations of certain branes. Our present study suggests a more fundamental and ubiquitous connection of string theory with the QHE in particular and with non-commutative geometry in general.…”

Section: Summary and Discussionmentioning

confidence: 99%

BPSR-balls in Script N = 4 SYM onR×S³, quantum Hall analogy and AdS/CFT holography

Dai¹,

Wang²,

Wu³

2006

J. High Energy Phys.

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In this paper, we propose a new approach to study the BPS dynamics in N = 4 supersymmetric U(N ) Yang-Mills theory on R × S 3 , in order to better understand the emergence of gravity in the gauge theory. Our approach is based on supersymmetric, space-filling Q-balls with R-charge, which we call R-balls. The usual collective coordinate method for non-topological scalar solitons is applied to quantize the half and quarter BPS R-balls. In each case, a different quantization method is also applied to confirm the results from the collective coordinate quantization. For finite N , the half BPS R-balls with a U(1) R-charge have a moduli space which, upon quantization, results in the states of a quantum Hall droplet with filling factor ν = 1. These states are known to correspond to the "sources" in the Lin-Lunin-Maldacena geometries in IIB supergravity. For large N , we find a new class of quarter BPS R-balls with a non-commutativity parameter. Quantization on the moduli space of such R-balls gives rise to a non-commutative ChernSimons matrix mechanics, which is known to describe a fractional quantum Hall system. In view of AdS/CFT holography, this demonstrates a profound connection of emergent quantum gravity with non-commutative geometry, of which the quantum Hall effect is a special case.

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“…It then follows from (2.14) and (2.22) that 18) namely that there are no strings. This is consistent with what was found in the spacetime viewpoint (3.11).…”

Section: Jhep11(2001)019mentioning

confidence: 98%

“…In particular the non-commutative SYM theory on the massless Type IIA D2-brane is obtained by considering fluctuations about a noncommutative configuration in the D-particle matrix model. Similarly, NCCS theory can also be obtained from a one-dimensional matrix model [18] …”

Section: D-particles and The Chern-simons Matrix Modelmentioning

confidence: 99%

The Stringy Quantum Hall Fluid

Brodie¹

2001

Self Cite

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Using branes in massive type IIA string theory, and a novel decoupling limit, we provide an explicit correspondence between non-commutative Chern-Simons theory and the fractional quantum Hall fluid. The role of the electrons is played by D-particles, the background magnetic field corresponds to a RR 2-form flux, and the two-dimensional fluid is described by non-commutative D2-branes. The filling fraction is given by the ratio of the number of D2-branes and the number of D8-branes, and therefore by the ratio rank/level of the Chern-Simons gauge theory. Quasiparticles and quasiholes are realized as endpoints of fundamental strings on the D2-branes, and are found to possess fractional D-particle charges and fractional statistics.

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How Bob Laughlin Tamed the Giant Graviton from Taub-NUT Space

Cited by 26 publications

References 19 publications

D1-strings in large RR 3-form flux, quantum Nambu geometry and M5-branes in theC-field

D1-strings in large RR 3-form flux, quantum Nambu geometry and M5-branes in theC-field

BPSR-balls in Script N = 4 SYM onR×S³, quantum Hall analogy and AdS/CFT holography

The Stringy Quantum Hall Fluid

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How Bob Laughlin Tamed the Giant Graviton from Taub-NUT Space

Cited by 26 publications

References 19 publications

D1-strings in large RR 3-form flux, quantum Nambu geometry and M5-branes in theC-field

D1-strings in large RR 3-form flux, quantum Nambu geometry and M5-branes in theC-field

BPSR-balls in Script N = 4 SYM onR×S3, quantum Hall analogy and AdS/CFT holography

The Stringy Quantum Hall Fluid

Contact Info

Product

Resources

About

BPSR-balls in Script N = 4 SYM onR×S³, quantum Hall analogy and AdS/CFT holography