Lorentz invariant and supersymmetric interpretation of noncommutative quantum field theory

Abstract

In this paper, using a Hopf-algebraic method, we construct deformed Poincaré SUSY algebra in terms of twisted (Hopf) algebra. By adapting this twist deformed super-Poincaré 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.

15 pages, LaTeX. v3:One section added, typos corrected, to appear in Int. J. Mod. Phys. A

References in corpus (8)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Non-commutative superspace from string theory
• Non(anti)commutative Superspace
• Supersymmetric Gauge Theories on Noncommutative Superspace
• Non-anticommutative N=2 super-Yang-Mills theory with singlet deformation
• Quasi-Hopf Superalgebras and Elliptic Quantum Supergroups

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• Deformed conformal and super-Poincaré symmetries in the non-(anti)commutative spaces
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