Noncommutative Electromagnetism As A Large N Gauge Theory
arXiv:0704.0929 · doi:10.1140/epjc/s10052-009-1117-9
Abstract
We map noncommutative (NC) U(1) gauge theory on R^d_C X R^{2n}_{NC} to U(N -> \infty) Yang-Mills theory on R^d_C, where R^d_C is a d-dimensional commutative spacetime while R^{2n}_{NC} is a 2n-dimensional NC space. The resulting U(N) Yang-Mills theory on R^d_C is equivalent to that obtained by the dimensional reduction of (d+2n)-dimensional U(N) Yang-Mills theory onto R^d_C. We show that the gauge-Higgs system (A_μ,Φ^a) in the U(N -> \infty) Yang-Mills theory on R^d_C leads to an emergent geometry in the (d+2n)-dimensional spacetime whose metric was determined by Ward a long time ago. In particular, the 10-dimensional gravity for d=4 and n=3 corresponds to the emergent geometry arising from the 4-dimensional N=4 vector multiplet in the AdS/CFT duality. We further elucidate the emergent gravity by showing that the gauge-Higgs system (A_μ,Φ^a) in half-BPS configurations describes self-dual Einstein gravity.
25 pages; More clarifications, to appear in Eur. Phys. J. C
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