D=2,N=2, Supersymmetric theories on Non(anti)commutative Superspace

Abstract

The classical action of a two dimensional N = 2 supersymmetric theory, characterized by a general Kähler potential, is written down on a non(anti)commutative superspace. The action has a power series expansion in terms of the determinant of the non(anti)commutativity parameter C αβ . The theory is explicitly shown to preserve half of the N = 2 supersymmetry, to all orders in (det C) n . The results are further generalized to include arbitrary superpotentials as well.

N=2σ -model action on non(anti)commutative superspace

“…The above action for the non(anti)commutative σ-models is a series expansion in (det C). Despite the presence of infinite terms, the action (3) has been shown be invariant under the N = 1/2 supersymmetry of the theory [13], which is a further check that the action in the component form is correct. For the special case of C = 0, the action in eqn.…”

“…(3). We note that I o and I c can be shown to be independenly invariant under N = 1/2 supersymmetry of the theory [13], and can be dealt seperately. We now use this fact to derive the equation of motion of auxiliary field F for the C-dependent and C-independent † Solutions to auxiliary fields in four dimensions have also been discussed in [19,20] parts seperately, from eqn.…”

“…To understand the conformal structure of non(anti)commutative theories in two dimensions, we studied the classical aspects of σ-models defined on non(anti)commutative (NAC) superspace with a general Kähler potential [13,14]. It was shown that due to the NAC deformation, the classical action has infinitely many terms.…”

“…We now use this fact to derive the equation of motion of auxiliary field F for the C-dependent and C-independent † Solutions to auxiliary fields in four dimensions have also been discussed in [19,20] parts seperately, from eqn. (13). Collecting terms proportional to zeroth and first order in (det C) on both sides of eqn.…”

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

“…Solitons, instanton solutions and some nonpertubative aspects were considered in [37][38][39][40][41][42]. The generalization to N = 2 and other interesting features have been explored in [43][44][45][46][47][48][49][50][51][52][53][54][55].…”