On the complete Seiberg-Witten map for theories with topological terms

Vilar, L. C. Q.; Ventura, O. S.; Amaral, R. L. P. G.; Lemes, V. E. R.; Buffon, L O

doi:10.1088/1126-6708/2007/04/018

Cited by 5 publications

(9 citation statements)

References 34 publications

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“…In the first one, Seiberg and Witten [1], inspired by the previously known result that the low energy limit of open strings could lead both to a gauge theory defined on a noncommutative space as well as to a usual commutative gauge theory, depending only on gauge choices, announced the existence of what became called the Seiberg-Witten map between noncommutative and commutative gauge theories. This achievement was then fully tested and confirmed by several authors in both the general structures of gauge transformations as in specific examples of gauge theories (we make a short list of references which is far from being complete [2][3][4][5][6][7][8][9][10][11]). It also opened a window to an alternative approach to the quantum properties of the noncommutative theories.…”

Section: Introductionmentioning

confidence: 61%

On the renormalizability of noncommutativeU(1) gauge theory—an algebraic approach

Vilar¹,

Ventura²,

Tedesco³

et al. 2010

J. Phys. A: Math. Theor.

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We investigate the quantum effects of the nonlocal gauge invariant operator 1 D 2 F µν * 1 D 2 F µν in the noncommutative U (1) action and its consequences to the infrared sector of the theory. Nonlocal operators of such kind were proposed to solve the infrared problem of the noncommutative gauge theories evading the questions on the explicit breaking of the Lorentz invariance. More recently, a first step in the localization of this operator was accomplished by means of the introduction of an extra tensorial matter field, and the first loop analysis was carried out (Eur.P hys.J.C62 : 433 − 443, 2009). We will complete this localization avoiding the introduction of new degrees of freedom beyond those of the original action by using only BRST doublets. This will allow us to make a complete BRST algebraic study of the renormalizability of the theory, following Zwanziger's method of localization of nonlocal operators in QFT. *

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Section: Introductionmentioning

confidence: 61%

On the renormalizability of noncommutativeU(1) gauge theory—an algebraic approach

Vilar¹,

Ventura²,

Tedesco³

et al. 2010

J. Phys. A: Math. Theor.

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“…We also mention that the Seiberg-Witten map for Chern-Simons gauge theories can be studied to all orders in the noncommutativity parameter θ [29], [30].…”

Section: Geometric Seiberg-witten Mapmentioning

confidence: 99%

“…Another source of ambiguities is related to field redefinitions of the gauge potential. Use of a nonstandard solution to SW map may lead to different results, see[25] where a nontrivial second order in θ expansion of the D = 3 CS action is constructed via a nonstandard solution to SW map.…”

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confidence: 99%

Noncommutative Chern-Simons gauge and gravity theories and their geometric Seiberg-Witten map

Aschieri

Castellani

2014

J. High Energ. Phys.

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We use a geometric generalization of the Seiberg-Witten map between noncommutative and commutative gauge theories to find the expansion of noncommutative Chern-Simons (CS) theory in any odd dimension D and at first order in the noncommutativity parameter θ. This expansion extends the classical CS theory with higher powers of the curvatures and their derivatives.A simple explanation of the equality between noncommutative and commutative CS actions in D = 1 and D = 3 is obtained. The θ dependent terms are present for D ≥ 5 and give a higher derivative theory on commutative space reducing to classical CS theory for θ → 0. These terms depend on the field strength and not on the bare gauge potential.In particular, as for the Dirac-Born-Infeld action, these terms vanish in the slowly varying field strength approximation: in this case noncommutative and commutative CS actions coincide in any dimension.The Seiberg-Witten map on the D = 5 noncommutative CS theory is explored in more detail, and we give its second order θ-expansion for any gauge group. The example of extended D = 5 CS gravity, where the gauge group is SU(2, 2), is treated explicitly.

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“…and a cohomological characterization of the general solution was accomplished in [3]. As a by-product of this study, a conjecture on the existence of SW maps taking noncommutative theories in the presence of topological terms into renormalizable commutative field theories was proposed.…”

Section: Introductionmentioning

confidence: 97%

“…The case of 3D theories was analysed in detail. It was shown how a map of the 3D noncommutative Maxwell theory in the presence of a noncommutative Chern-Simons term (NCCSM) would lead to the usual commutative theory [3], whereas θ -dependent nonrenormalizable interactions inevitably accompany the SW mapped noncommutative Maxwell theory (NCM) theory in the absence of a topological sector [4].…”

Section: Introductionmentioning

confidence: 99%