Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-03-04
Phys.Rev.D74:085027,2006
Physics
High Energy Physics
High Energy Physics - Theory
15 pages, revtex4. v.2: We added a proof that the terms in (4.9) are not surface terms, a new paragraph in our conclusion and
Scientific paper
10.1103/PhysRevD.74.085027
We extend the ordinary 3D electromagnetic duality to the noncommutative (NC) space-time through a Seiberg-Witten map to second order in the noncommutativity parameter (theta), defining a new scalar field model. There are similarities with the 4D NC duality, these are exploited to clarify properties of both cases. Up to second order in theta, we find that duality interchanges the 2-form theta with its 1-form Hodge dual *theta times the gauge coupling constant, i.e., theta --> *theta g^2 (similar to the 4D NC electromagnetic duality). We directly prove that this property is false in the third order expansion in both 3D and 4D space-times, unless the slowly varying fields limit is imposed. Outside this limit, starting from the third order expansion, theta cannot be rescaled to attain an S-duality. In addition to possible applications on effective models, the 3D space-time is useful for studying general properties of NC theories. In particular, in this dimension, we deduce an expression that significantly simplifies the Seiberg-Witten mapped Lagrangian to all orders in theta.
Rodrigues D. C. D.
Wotzasek Clovis
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