Recent Results on N=2,4 Supersymmetry with Lorentz Symmetry Violating

In this work, we propose the N=2 and N=4 supersymmetric extensions of the Lorentz-breaking Abelian Chern-Simons term. We formulate the question of the Lorentz violation in 6 and 10 dimensions to obtain the bosonic sectors of N=2, and N=4, supersymmetries, respectively. From this, we carry out an analysis in N=1, D=4 superspace and, in terms of N=1, superfields, we are able to write down the N=2 and N=4 supersymmetric versions of the Lorentz-violating action term.

In this work, we propose the N=2 and N=4 supersymmetric extensions realized off-shell of the Abelian gauge model with Chern-Simons Lorentz-breaking term. We start with the theory in 6 and 10 dimensions and reduce \`{a} la Scherk the space-like coordinates to carry out the D=5 model in both cases. Then, we reduce the fifth space-like coordinate using the Legendre transformation technique for dimensional reduction. The last reduction method provides us with auxiliary fields tha...

Broken spacetime symmetries might emerge from a fundamental physical theory. The effective low-energy theory might be expected to exhibit violations of supersymmetry and Lorentz invariance. Some illustrative models which combine supersymmetry and Lorentz violation are described, and a superspace formulation is given.

We discuss three manners to implement Lorentz symmetry breaking in a superfield theory formulated within the superfield formalism, that is, deformation of the supersymmetry algebra, introducing of an extra superfield whose components can depend on Lorentz-violating (LV) vectors (tensors), and adding of new terms proportional to LV vectors (tensors) to the superfield action. We illustrate these methodologies with examples of quantum calculations.

Some additional references are included on the last 3 pages.

We extend Lorentz-violating Supersymmetry models to include vector superfields. The CPT-preserving model generalizes easily, while the obvious attempt at generalizing the CPT-violating model meets serious obstructions. Generalizations of the CPT-preserving but Lorentz-Violating model to higher dimensions are also straightforward. Compactification is used to reduce the six-dimensional theory to an ${\cal{N}} =2$ Lorentz-violating theory in four dimensions, while the ten-dimens...

We construct supersymmetric Lorentz violating operators for matter and gauge fields. We show that in the supersymmetric Standard Model the lowest possible dimension for such operators is five, and therefore they are suppressed by at least one power of an ultra--violet energy scale, providing a possible explanation for the smallness of Lorentz violation and its stability against radiative corrections. Supersymmetric Lorentz noninvariant operators do not lead to modifications o...

In this work, we present two possible venues to accomodate the $K_{F}$-type Lorentz-symmetry violating Electrodynamics in an $N=1$-supersymmetric framework. A chiral and a vector superfield are chosen to describe the background that signals Lorentz-symmetry breaking. In each case, the $\ K_{\mu \nu \kappa \lambda }$-tensor is expressed in terms of the components of the background superfield that we choose to describe the breaking. We also present in detail the actions with al...

These five lectures collect elementary facts about 4D supersymmetric theories with emphasis on N=1 supersymmetry, as well as the basic notions of supersymmetric quantum mechanics. Contents: I. From symmetries to supersymmetry; II. Basic features of supersymmetry; III. Representations of supersymmetry; IV. Superspace and superfields; V. Supersymmetric quantum mechanics.

The standard forms of supersymmetry and supergravity are inextricably wedded to Lorentz invariance. Here a Lorentz-violating form of supergravity is proposed. The superpartners have exotic properties that are not possible in a theory with exact Lorentz symmetry and microcausality. For example, the bosonic sfermions have spin 1/2 and the fermionic gauginos have spin 1. The theory is based on a phenomenological action that is shown to follow from a simple microscopic and statis...