Drinfel'd Twisted Superconformal Algebra and Structure of Unbroken Symmetries

We investigate deformed superconformal symmetries on non(anti)commutative (super)spaces from the point of view of the Drinfel'd twisted symmetries. We classify all possible twist elements derived from an abelian subsector of the superconformal algebra. The symmetry breaking caused by the non(anti)commutativity of the (super)spaces is naturally interpreted as the modification of their coproduct emerging from the corresponding twist element. The remaining unbroken symmetries are determined by the commutative properties of those symmetry generators possessing the twist element. We also comment on non-canonically deformed non(anti)commutative superspaces, particularly those derived from the superconformal twist element (\mathcal{F}_{\mathrm{SS}}).Comment: 13 pages, LaTeX; typos of published version and references are correcte

Time-dependent and Non-BPS Solutions in N=6 Superconformal Chern-Simons Theory

We study a class of classical solutions of three-dimensional N=6 superconformal Chern-Simons theory coupled with U(N) \times U(N) bi-fundamental matter fields. Especially, time evolutions of fuzzy spheres are discussed for both massless and massive cases. For the massive case, there are a variety of solutions having different behaviors according to the value of the mass. In addition to the time-dependent solutions, we analyze non-BPS static solutions which represent parallel M5/M5 or M5/anti-M5-branes suspended by multiple M2-branes. These solutions are similar to the fundamental strings connecting two parallel (anti) Dp-branes in perturbative string theory. A moving M5-brane and domain wall solutions with constant velocity that are obtained by the Lorentz boost of the known BPS solutions are briefly addressed.Comment: 27 pages, 9 figures, published version in JHE

Non-local Wess-Zumino Model on Nilpotent Noncommutative Superspace

We investigate the theory of the bosonic-fermionic noncommutativity, $[x^{\mu},\theta^{\alpha}] = i \lambda^{\mu \alpha}$, and the Wess-Zumino model deformed by the noncommutativity. Such noncommutativity links well-known space-time noncommutativity to superspace non-anticommutativity. The deformation has the nilpotency. We can explicitly evaluate noncommutative effect in terms of new interactions between component fields. The interaction terms that have Grassmann couplings are induced. The noncommutativity does completely break full $\mathcal{N}=1$ supersymmetry to $\mathcal{N} = 0$ theory in Minkowski signature. Similar to the space-time noncommutativity, this theory has higher derivative terms and becomes non-local theory. However this non-locality is milder than the space-time noncommutative field theory. Due to the nilpotent feature of the coupling constants, we find that there are only finite number of Feynman diagrams that give noncommutative corrections at each loop order.Comment: Latex, 16 pages, 2 figures, typos corrected, some references and comments on auxiliary field added, a figure replaced, English refine

Lorentz invariant and supersymmetric interpretation of noncommutative quantum field theory

In this paper, using a Hopf-algebraic method, we construct deformed Poincar\'e SUSY algebra in terms of twisted (Hopf) algebra. By adapting this twist deformed super-Poincar\'e algrebra as our fundamental symmetry, we can see the consistency between the algebra and non(anti)commutative relation among (super)coordinates and interpret that symmetry of non(anti)commutative QFT is in fact twisted one. The key point is validity of our new twist element that guarantees non(anti)commutativity of space. It is checked in this paper for N=1 case. We also comment on the possibility of noncommutative central charge coordinate. Finally, because our twist operation does not break the original algebra, we can claim that (twisted) SUSY is not broken in contrast to the string inspired $\mathcal{N}=1/2$ SUSY in N=1 non(anti)commutative superspace.Comment: 15 pages, LaTeX. v3:One section added, typos corrected, to appear in Int. J. Mod. Phys.

Non-Anti-Commutative deformation of effective potentials in supersymmetric gauge theories

We studied a nilpotent Non-Anti-Commutative (NAC) deformation of the effective superpotentials in supersymmetric gauge theories, caused by a constant self-dual graviphoton background. We derived the simple non-perturbative formula applicable to any NAC (star) deformed chiral superpotential. It is remarkable that the deformed superpotential is always `Lorentz'-invariant. As an application, we considered the NAC deformation of the pure super-Yang-Mills theory whose IR physics is known to be described by the Veneziano-Yankielowicz superpotential (in the undeformed case). The unbroken gauge invariance of the deformed effective action gives rise to severe restrictions on its form. We found a non-vanishing gluino condensate in vacuum but no further dynamical supersymmetry breaking in the deformed theory.Comment: 20 pages, LaTeX; small changes, additions and references adde

N=1/2 supersymmetric four-dimensional non-linear sigma-models from non-anti-commutative superspace

The component structure of a generic N=1/2 supersymmetric Non-Linear Sigma-Model (NLSM) defined in the four-dimensional (Euclidean) Non-Anti-Commutative (NAC) superspace is investigated in detail.The most general NLSM is described in terms of arbitrary K"ahler potential,and chiral and anti-chiral superpotentials. The case of a single chiral superfield gives rise to splitting of the NLSM potentials, whereas the case of several chiral superfields results in smearing (or fuzziness) of the NLSM potentials, while both effects are controlled by the auxiliary fields. We eliminate the auxiliary fields by solving their algebraic equations of motion, and demonstrate that the results are dependent upon whether the auxiliary integrations responsible for the fuzziness are performed before or after elimination of the auxiliary fields. There is no ambiguity in the case of splitting, i.e. for a single chiral superfield. Fully explicit results are derived in the case of the N=1/2 supersymmetric NAC-deformed CP(n) NLSM in four dimensions. Here we find another surprise that our results differ from the N=1/2 supersymmetric CP(n) NLSM derived by the quotient construction from the N=1/2 supersymmetric NAC-deformed gauge theory. We conclude that an N=1/2 supersymmetric deformation of a generic NLSM from the NAC superspace is not unique.Comment: 16 pages, LaTeX, no figure