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arXiv · hep-th/0605188

BPS R-balls in N=4 SYM on R X S^3, Quantum Hall Analogy and AdS/CFT Holography

Jian Dai·Xiao-Jun Wang·Yong-Shi Wu
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Abstract

In this paper, we propose a new approach to study the BPS dynamics in N=4 supersymmetric U(N) Yang-Mills theory on R X 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 one. 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 Chern-Simons 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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Jian Dai, Xiao-Jun Wang, Yong-Shi Wu. 2006-06-08. BPS R-balls in N=4 SYM on R X S^3, Quantum Hall Analogy and AdS/CFT Holography. https://doi.org/10.1088/1126-6708%2F2006%2F06%2F060

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