# A new approach to the analysis of a noncommutative Chern-Simons theory

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Anirban Saha, Apr 18, 2014 Available from:-
##### Article: Noncommutative Solitons of Gravity

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**ABSTRACT:**We investigate a three-dimensional gravitational theory on a noncommutative space which has a cosmological constant term only. We found various kinds of nontrivial solutions, by applying a similar technique which was used to seek noncommutative solitons in noncommutative scalar field theories. Some of those solutions correspond to bubbles of spacetimes, or represent dimensional reduction. The solution which interpolates $G_{\mu\nu}=0$ and Minkowski metric is also found. All solutions we obtained are non-perturbative in the noncommutative parameter $\theta$, therefore they are different from solutions found in other contexts of noncommutative theory of gravity and would have a close relation to quantum gravity.Classical and Quantum Gravity 11/2009; DOI:10.1088/0264-9381/27/10/105014 · 3.10 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We find a closed form for Seiberg-Witten (SW) map between ordinary and noncommutative (NC) Dirac-Born-Infeld actions. We show that NC Maxwell action after the exact SW map can be regarded as ordinary Maxwell action coupling to a metric deformed by gauge fields. We also show that reversed procedure by inverse SW map leads to a similar interpretation in terms of induced NC geometry. This implies that noncommutativity in field theory can be interpreted as field dependent fluctuations of spacetime geometry, which genuinely realizes an interesting idea recently observed by Rivelles. Comment: 12 pages, Latex; version to appear in Mod. Phys. Lett. AModern Physics Letters A 02/2004; 21(35). DOI:10.1142/S0217732306021682 · 1.34 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We consider 2+1 dimensional noncommutative models of scalar and fermionic fields coupled to the Chern-Simons field. We show that, at least up to one loop, the model containing only a fermionic field in the fundamental representation minimally coupled to the Chern-Simons field is consistent in the sense that there are no nonintegrable infrared divergences. By contrast, dangerous infrared divergences occur if the fermion field belongs to the adjoint representation or if the coupling of scalar matter is considered instead. The superfield formulation of the supersymmetric Chern-Simons model is also analyzed and shown to be free of nonintegrable infrared singularities and actually finite if the matter field belongs to the fundamental representation of the supergauge group. In the case of the adjoint representation this only happens in a particular gauge. Comment: minor corrections and some references addedPhysical review D: Particles and fields 10/2004; 71(10). DOI:10.1103/PhysRevD.71.105005 · 4.86 Impact Factor