BPS - type Equations in the Non - anticommutative N = 2 Supersymmetric U ( 1 ) Gauge Theory 1

We investigate the equations of motion in the four-dimensional non-anticommutative N=2 supersymmetric U(1) gauge field theory, in the search for BPS configurations. The BPS-like equations, generalizing the abelian (anti)self-duality conditions, are proposed. We prove full solvability of our BPS-like equations, as well their consistency with the equations of motion. Certain restrictions on the allowed scalar field values are also found. Surviving supersymmetry is briefly discussed too. Supported in part by the JSPS and the Volkswagen Stiftung Email address: [email protected] Email address: [email protected]