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Gravitational instantons from gauge theory.
Hyun Seok Yang1, Mario Salizzoni
1Institut für Physik, Humboldt Universität zu Berlin, Newtonstrasse 15, D-12489 Berlin, Germany. hsyang@physik.hu-berlin.de
Physical Review Letters
|June 29, 2006
Summary
Noncommutative (NC) gauge theories on noncommutative spacetimes are equivalent to ordinary gauge theories via the Seiberg-Witten map. This study shows NC U(1) instantons map to gravitational instantons, linking NC gauge theory to hyper-Kähler geometries.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
- String Theory
Background:
- Gauge theories can be formulated on noncommutative (NC) spacetimes.
- The Seiberg-Witten (SW) map provides a dual description of NC gauge theories in terms of ordinary gauge theories on commutative spacetimes.
Purpose of the Study:
- To investigate the relationship between NC U(1) instantons and gravitational instantons using the exact SW map.
- To explore the equivalence between NC U(1) gauge theory and hyper-Kähler geometries.
Main Methods:
- Application of the exact Seiberg-Witten map to Nekrasov-Schwarz type NC U(1) instantons.
- Analysis of the resulting dual description in terms of ordinary gauge theory.
Main Results:
- All NC U(1) instantons are mapped to asymptotically locally Euclidean (ALE) gravitational instantons by the exact SW map.
- The NC gauge theory of U(1) instantons is shown to be equivalent to the theory of hyper-Kähler geometries.
Conclusions:
- ALE gravitational instantons can emerge from local condensates of purely NC photons.
- Establishes a profound connection between noncommutative gauge theories and hyper-Kähler geometry.