Duals of noncommutative supersymmetric U(1) gauge theory

Classically, the dual under the Seiberg-Witten map of noncommutative U(N), N = 1 super Yang-Mills theory is a field theory with ordinary gauge symmetry whose fields carry, however, a θ -deformed nonlinear realisation of the N = 1 supersymmetry algebra in four dimensions. For the latter theory we work out at one-loop and first order in the noncommutative parameter matrix θ µν the UV divergent part of its effective action in the background-field gauge, and, for N = 1 , we show that for finite values of N the gauge sector fails to be renormalisable; however, in the large N limit the full theory is renormalisable, in keeping with the expectations raised by the quantum behaviour of the theory's noncommutative classical dual. We also obtain -for N ≥ 3 , the case with N = 2 being trivial-the UV divergent part of the effective action of the SU(N) noncommutative theory in the enveloping-algebra formalism that is obtained from the previous ordinary U(N) theory by removing the U(1) degrees of freedom. This noncommutative SU(N) theory is also renormalisable.

Section: Jhep11(2009)092mentioning

confidence: 99%

Noncommutative 𝒩 = 1 super Yang-Mills, the Seiberg-Witten map and UV divergences

Martı́n

Tamarit

2009

“…In refs. [14] and [18] it is claimed that there exists such a generalisation and that it is a polynomial -and thus a local object -in the ordinary vector superfield and its supersymmetry covariant derivatives. This statement is at odds with the result presented in ref.…”

Section: Jhep11(2008)087mentioning

confidence: 99%

“…Such ordinary dual theory is constructed in refs. [17,18] and [20]. In these papers, the transformations of the fields of the dual ordinary theory that give rise to the supersymmetry transformations of the noncommutative theory are computed at first-order in the noncommutativity parameters.…”

Section: Jhep11(2008)087mentioning

confidence: 99%

The Seiberg-Witten map and supersymmetry

Martı́n¹,

Tamarit²

2008

The lack of any local solution to the first-order-in-hω mn Seiberg-Witten (SW) map equations for U(1) vector superfields compels us to obtain the most general solution to those equations that is a quadratic polynomial in the ordinary vector superfield, v , its chiral and antichiral projections and the susy covariant derivatives of them all. Furnished with this solution, which is local in the susy Landau gauge, we construct an ordinary dual of noncommutative U(1) SYM in terms of ordinary fields which carry a linear representation of the N = 1 susy algebra. By using the standard SW map for the N = 1 U(1) gauge supermultiplet we define an ordinary U(1) gauge theory which is dual to noncommutative U(1) SYM in the WZ gauge. We show that the ordinary dual so obtained is supersymmetric, for, as we prove as we go along, the ordinary gauge and fermion fields that we use to define it carry a nonlinear representation of the N = 1 susy algebra. We finally show that the two ordinary duals of noncommutative U(1) SYM introduced above are actually the same N = 1 susy gauge theory. We also show in this paper that the standard SW map is never the θ θ component of a local superfield in v and check that, at least at a given approximation, a suitable field redefinition of that map makes the noncommutative and ordinary -in a B mn field-susy U(1) DBI actions equivalent.

“…These equations have the same form as the homogenous Seiberg-Witten equations in the case of canonically deformed superspace [56,60,61]. However, we can not simply take the known homogenous solutions from canonically deformed superspace since the mass dimension of the noncommutativity parameters differs.…”

Section: Construction Of the Seiberg-witten Map In Terms Of Componentmentioning

confidence: 99%

Seiberg-Witten Map for Superfields onN=(1/2,0) andN=(1/2,1/2) Deformed Superspace

Mikulovic¹

2004

In this paper we construct the Seiberg-Witten maps for superfields on the θ − θ deformed superspaces with N = ( 1 2 , 0) and N = ( 1 2 , 1 2 ) supersymmety. We show that on the N = ( 1 2 , 0) deformed superspace there is no SeibergWitten map for antichiral superfields which is at the same time antichiral, local and which preserves the N = ( 1 2 , 0) supersymmetry. Solutions which break this requirements are presented. On the N = ( 1 2 , 1 2 ) deformed superspace we show that for the chiral gauge parameter, and therefore also for the chiral matter field, there is no chiral Seiberg-Witten map. Some other possible Seiberg-Witten maps for the superfields are presented.