Dynamics of giant-gravitons in the LLM geometry and the fractional quantum Hall effect

Abstract

The LLM's 1/2 BPS solutions of IIB supergravity are known to be closely related to the integer quantum Hall droplets with filling factor ν = 1, and the giant gravitons in the LLM geometry behave like the quasi-holes in those droplets. In this paper we consider how the fractional quantum Hall effect may arise in this context, by studying the dynamics of giant graviton probes in a special LLM geometry, the AdS 5 × S 5 background, that corresponds to a circular droplet. The giant gravitons we study are D3-branes wrapping on a 3-sphere in S 5 . Their low energy world-volume theory, truncated to the 1/2 BPS sector, is shown to be described by a Chern-Simons finite-matrix model. We demonstrate that these giant gravitons may condense at right density further into fractional quantum Hall fluid due to the repulsive interaction in the model, giving rise to the new states in IIB string theory. Some features of the novel physics of these new states are discussed.

1/4-BPS M-theory bubbles with SO(3) × SO(4) symmetry

“…It is also very important to find the connection of our results with the dual field theory dynamics. For 1/2-BPS bubbles of IIB theory, where the field theory is amenable to perturbative analysis since it is reduced to a hermitian matrix model, there has been considerable progress in relating the Yang-Mills theory with the semiclassical treatment of IIB supergravity theory [22,23,24,25,26,27]. See also [28] for analogous discussions on bubbles of AdS 3 × S 3 .…”

LargeNspectrum of two matrices in a harmonic potential and BMN energies

“…We now wish to calculate the first order perturbation theory correction to the free energy J + 2 of the BMN operator above. For this, we write (35) in terms of our hermitean variables (34) after noticing that the rescaling (7) requires that we let M → √ NM. The interaction Hamiltonian then takes the form:…”

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

“…The above figure motivates us to suggest the following picture: The G-particles, thought of as "sources" in IIB supergravity like LLM particles in the LLM construction, form a four dimensional object: namely we have a bunch (N 2 ) of FQH droplets, each living on the Z 1 -plane, consisting of N 1 G-particles and looking like a point-like object on the Z 2 -plane; and the bunch of N 2 point-like objects also form a FQH droplet on the Z 2 -plane. This state is certainly not the FQH state of LLM fermions that the present authors suggested in the IIB quantum gravity about a year ago [9], which is known as a deformation of the 1/2 BPS IIB geometry to have null singularity. The above picture for the states (6.10) immediately suggests themselves as a resolution of our previously proposed FQH states of LLM fermions: Namely in the limit N 1 , N 2 → ∞ with fixed N 2 /N 1 = q/p 0, the quantum states (6.10) become a candidate for the SYM dual of the FQH states in IIB gravity suggested by us [9].…”

“…This state is certainly not the FQH state of LLM fermions that the present authors suggested in the IIB quantum gravity about a year ago [9], which is known as a deformation of the 1/2 BPS IIB geometry to have null singularity. The above picture for the states (6.10) immediately suggests themselves as a resolution of our previously proposed FQH states of LLM fermions: Namely in the limit N 1 , N 2 → ∞ with fixed N 2 /N 1 = q/p 0, the quantum states (6.10) become a candidate for the SYM dual of the FQH states in IIB gravity suggested by us [9]. Indeed, we can present several evidences for this suggestion:…”

“…At the zeroth order, we have only H 1 , which describes a 2d FQH system, as what we have suggested in ref. [9].…”