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

TL;DR

This paper introduces a novel approach using supersymmetric R-balls in N=4 SYM to explore emergent gravity, revealing connections to quantum Hall systems and non-commutative geometry within the AdS/CFT framework.

Contribution

It develops a new quantization method for BPS R-balls, linking gauge theory states to quantum Hall droplets and non-commutative Chern-Simons mechanics, advancing understanding of holographic emergence of gravity.

Findings

Half BPS R-balls correspond to quantum Hall droplet states.

Large N quarter BPS R-balls relate to non-commutative Chern-Simons mechanics.

Connection established between quantum Hall effects and emergent quantum gravity.

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.