Twisted supersymmetry in a deformed Wess-Zumino model in (2 + 1) dimensions

Abstract

Non-anticommutative deformations have been studied in the context of supersymmetry (SUSY) in three and four space-time dimensions, and the general picture is that highly nontrivial to deform supersymmetry in a way that still preserves some of its important properties, both at the formal algebraic level (e.g., preserving the associativity of the deformed theory) as well as at the physical level (e.g., maintaining renormalizability). The Hopf algebra formalism allows the definition of algebraically consistent deformations of SUSY, but this algebraic consistency does not guarantee that physical models build upon these structures will be consistent from the physical point of view. We will investigate a deformation induced by a Drinfel'd twist of the N = 1 SUSY algebra in three space-time dimensions. The use of the Hopf algebra formalism allows the construction of deformed N = 1 SUSY algebras that should still preserve a deformed version of supersymmetry. We will construct the simplest deformed version of the Wess-Zumino model in this context, but we will show that despite the consistent algebraic structure, the model in question is not invariant under SUSY transformation and is not renormalizable. We will comment on the relation of these results with previous ones discussed in the literature regarding similar four-dimensional constructions.

Aharonov-Bohm scattering for relativistic particles in (3 + 1)-dimensional noncommutative space with spin dependence

“…With the advent of string theory, new interest in noncommutative (NC) space emerged. [6][7][8][9][10][11][12][13][14][15][16][17][18] It has been shown that the dynamics of open strings in the presence of an antisymmetric Bfield can be described in certain limits by a gauge theory on a noncommutative spacetime, 3 namely, one deformed by the Moyal product (whose definition will be given shortly).…”

$CP^{(N-1)}$ model in aether-superspace

“…As a matter of fact, the supersymmetry algebra is highly constrained, and as a consequence supersymmetric models themselves are also very constrained regarding possible terms in the classical Lagrangian and the quantum corrections, which is the main reason that some problematic contributions are avoided in many of the contexts mentioned above. For the same reason, consistent deformations of the supersymmetry algebra are not trivial do obtain, some noteworthy examples involving the use of Hopf algebras [12][13][14][15][16][17].…”