Nonequivalent Seiberg?Witten maps for noncommutative massive U(N) gauge theory

Abstract

Massive vector fields can be described in a gauge invariant way with the introduction of compensating fields. In the unitary gauge one recovers the original formulation. Although this gauging mechanism can be extended to noncommutative spaces in a straightforward way, non trivial aspects show up when we consider the Seiberg-Witten map. As we show here, only a particular class of its solutions leads to an action that admits the unitary gauge fixing.

Non-commutative Maxwell–Chern–Simons theory in three dimensions and its dual

“…We also note that the MCS coupling constant g 2 and the Chern-Simons parameter µ have both appeared as inverse couplings when compared with (20). We can now fix the gauge invariance in (24), for instance by choosing the unitary gauge Λ = 0, to recover the self-dual model given in (20). We thus conclude that the U (1) invariant MCS theory is dual to the U(1) invariant Stückelberg formulation of self-dual model.…”

“…In [24] the SW map for the NC Stückelberg-Proca theory has been obtained by requiring that in the unitary gauge it gives the Proca theory. Using the same criterion, the SW map for the NC Stückelberg-SD model is found to bê…”

Duality in Noncommutative Maxwell-Chern-Simons Theory

“…In [13] the SW map for the NC Stückelberg-Proca theory has been obtained by requiring that in the unitary gauge it gives the Proca theory. Using the same criterion, the SW map for the NC Stückelberg-SD model is found to bê …”