Seiberg-Witten maps to all orders

Abstract

All order Seiberg-Witten maps of gauge parameter, gauge field and matter fields are given as a closed recursive formula. These maps are obtained by analyzing the order by order solutions of the gauge consistency and equivalence conditions as well as by directly solving Seiberg-Witten differential equations. The explicit third order non-abelian and fourth order abelian Seiberg-Witten maps of gauge parameter and gauge field are also presented..

On the All Order Solutions of Seiberg-Witten Map for Noncommutative Gauge Theories

“…On the other hand, the solution of SW-map to all orders in θ for the gauge field, matter field (both in adjoint and fundamental representation) and the gauge parameter is given in Ref. 12. These solutions match with the second order solutions given in Ref.s 6-10.…”

“…12, it is also shown that these solutions (22-24) can be obtained by directly solving the respective Seiberg-Witten differential equation that can be obtained by varying the deformation parameter infinitesimally θ → θ + δθ for gauge fields…”

Spinning black holes in a gauge theory of gravitation

“…[4] and exploiting the results of Ref. [5]. Under the analytical procedure, we take an r-θ noncommutativite parameter because the gauge fields depend on 3D radius r and on θ and, in the case of nonrotating black holes [6], [7] lead to a diagonal noncommutative analogue metric tensor.…”

“…The first order corrections for tetrads, spin connection and field strength enters in the recursive formulas, [5] …”

Pair production of Dirac particles in a $$d+1$$ d + 1 -dimensional noncommutative space–time

“…Like in ordinary space-time, a gauge theory can be defined on a NC space-time [34] see also [35][36][37][38][39] and references therein. In the sequel, the NC variables are denoted with a "hat" notation.…”