Non-commutativity and Supersymmetry

We study the extent to which the gauge symmetry of abelian Yang-Mills can be deformed under two conditions: first, that the deformation depend on a two-form scale. Second, that the deformation preserve supersymmetry. We show that (up to a single parameter) the only allowed deformation is the one determined by the star product. We then consider the supersymmetry algebra satisfied by NCYM expressed in commutative variables. The algebra is peculiar since the supercharges are not gauge-invariant. However, the action, expressed in commutative variables, appears to be quadratic in fermions to all orders in θ.

[1]  D. Tsimpis,et al.  Spinorial cohomology and maximally supersymmetric theories , 2001, hep-th/0110069.

[2]  M. Douglas,et al.  Noncommutative field theory , 2001, hep-th/0106048.

[3]  D. Klemm,et al.  Non(anti)commutative superspace , 2001, hep-th/0104190.

[4]  M. Pernici,et al.  The one-loop effective action of noncommutative super Yang–Mills is gauge invariant , 2000, hep-th/0011140.

[5]  Hong Liu.  ∗-Trek II: ∗n operations, open Wilson lines and the Seiberg–Witten map , 2000, hep-th/0011125.

[6]  J. Michelson,et al.  ∗-Trek: the one-loop N=4 noncommutative SYM action , 2000, hep-th/0008205.

[7]  D. Gross,et al.  Dynamics of strings in noncommutative gauge theory , 2000, hep-th/0007204.

[8]  S. Rey,et al.  S-duality, noncritical open string and noncommutative gauge theory , 2000, Physics Letters B.

[9]  G. Rajesh,et al.  Duality and noncommutative gauge theory , 2000, hep-th/0005046.

[10]  E. Witten,et al.  String theory and noncommutative geometry , 1999, hep-th/9908142.

[11]  S. Paban,et al.  Supersymmetry and higher derivative terms in the effective action of Yang-Mills theories , 1998, hep-th/9806028.

[12]  S. Paban,et al.  Constraints from extended supersymmetry in quantum mechanics , 1998, hep-th/9805018.

[13]  Alain Connes,et al.  Noncommutative Geometry and Matrix Theory: Compactification on Tori , 1997, hep-th/9711162.

[14]  J. Schwarz,et al.  Gauge invariant and gauge fixed D-brane actions , 1996, hep-th/9612080.

[15]  R. R. Metsaev,et al.  Fermionic terms in the open superstring effective action , 1987 .

[16]  A. Tseytlin,et al.  The {Born-Infeld} Action as the Effective Action in the Open Superstring Theory , 1987 .