https://doi.org/10.1140/epjc/s10052-009-1117-9
Regular Article - Theoretical Physics
Noncommutative electromagnetism as a large N gauge theory
Institut für Physik, Humboldt Universität zu Berlin, Newtonstraße 15, 12489, Berlin, Germany
* e-mail: hsyang@kias.re.kr
Received:
12
March
2009
Revised:
29
June
2009
Published online:
16
October
2009
We map noncommutative (NC) U(1) gauge theory on ℝ
C
d
×ℝ
NC
2n
to U(N→∞) Yang–Mills theory on ℝ
C
d
, where ℝ
C
d
is a d-dimensional commutative spacetime while ℝ
NC
2n
is a 2n-dimensional NC space. The resulting U(N) Yang–Mills theory on ℝ
C
d
is equivalent to that obtained by the dimensional reduction of (d+2n)-dimensional U(N) Yang–Mills theory onto ℝ
C
d
. We show that the gauge-Higgs system (A
μ
,Φ
a
) in the U(N→∞) Yang–Mills theory on ℝ
C
d
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 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.
PACS: 11.10.Nx – / 02.40.Gh – / 04.50.+h –
© Springer-Verlag, 2009