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

We provide a pedagogical introduction to $N=1$ supergravity/supersymmetry in relation to particle physics. The various steps in the construction of a generic $N=1$ supergravity model are briefly described, and we focus on its low energy supersymmetric limit. The conditions for supersymmetry and supergravity breaking are investigated, and realistic mechanisms suitable for particle physics identified. We then study the model-building aspects of `softly-broken' supersymmetric ex...

We review the last year progress in understanding supersymmetric SU(2) Yang-Mills quantum mechanics in four and ten space-time dimensions. The four dimensional system is now well under control and the precise spectrum is obtained in all channels. In D=10 some new results are also available.

Here I briefly discuss why supersymmetry is considered a leading candidate of physics beyond the standard model. I also highlight the salient features of different supersymmetry breaking models. A few other symmetries, broken or intact, asscociated with any realistic supersymmetric model are also identified. This write-up is too simple-minded for an expert on supersymmetry. It is basically intended for those who are busy in other areas of high energy physics.

We study N=2 supersymmetric Chern-Simons Higgs models in $(2+1)$-dimensions. As we will demonstrate, an extended supersymmetric quantum mechanics algebras underlies the fermionic zero modes quantum system and the zero modes corresponding to bosonic fluctuations. These two algebras, in turn, combine to give an N=4 extended 1-dimensional supersymmetric algebra with central charge

This article reviews the subject of supersymmetry and its breaking. The emphasis is on recent developments in metastable, dynamical supersymmetry breaking, which permit the construction of promising models of particle physics.

Theory of Supersymmetric Quantum Electrodynamics is extended by interactions with external vector and tensor backgrounds, that are assumed to be generated by some Lorentz-violating (LV) dynamics at an ultraviolet scale perhaps related to the Planck scale. Exact supersymmetry requires that such interactions correspond to LV operators of dimension five or higher, providing a solution to the naturalness problem in the LV sector. We classify all dimension five and six LV operator...

Abstrct: We show that the action of self-dual supersymmetric Yang-Mills theory in four-dimensions, which describes the consistent massless background fields for $~N=2$~ superstring, generates the actions for $~N=1$~ and $~N=2$~ supersymmetric non-Abelian Chern-Simons theories in three-dimensions after appropriate dimensional reductions. Since the latters play important roles for supersymmetric integrable models, this result indicates the fundamental significance of the $~N=2$...

We construct N=1 supersymmetric field theory in 4+2 dimensions compatible with the theoretical framework of 2T physics and its gauge symmetries. The fields are arranged into 4+2 dimensional chiral and vector supermultiplets, and their interactions are uniquely fixed by SUSY and 2T-physics gauge symmetries. In a particular gauge the 4+2 theory reduces to ordinary supersymmetric field theory in 3+1 dimensions without any Kaluza-Klein remnants, but with some additional constrain...

In these lectures we present a detailed description of various aspects of gauge theories with extended N=2 and N=4 supersymmetry that are at the basis of recently found exact results. These results include the exact calculation of the low energy effective action for the light degrees of freedom in the N=2 super Yang-Mills theory and the conjecture, supported by some checks, that the N=4 super Yang-Mills theory is dual in the sense of Montonen-Olive.

We show in this paper that the dynamics of a non-relativistic particle with spin, coupled to an external electromagnetic field and to a background that breaks Lorentz symmetry, is naturally endowed with an N=1-supersymmetry. This result is achieved in a superspace approach where the particle coordinates and the spin degrees of freedom are components of the same supermultiplet.