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Reminiscences on the String origins of Supersymmetry are followed by a discussion of the importance of confusing bosons with fermions in building superstring theories in 9+1 dimensions. In eleven dimensions, the kinship between bosons and…
The difficulties of defining chiral gauge theories non-perturbatively suggest a vector-like extension of the standard model with three mirror fermion families. Some phenomenological implications of such an extension are discussed.
In addition to the very good theoretical motivations for supersymmetry, there are now at least nine phenomenological indications that nature is supersymmetric. All are indirect, so more is better. They are enumerated here. Some discussion…
Several ideas for solving the problem of fermion mass hierarchy and mixing and specific supersymmetric models that realize it are reviewed. In particular, we discuss many models based on SO(10) in four dimensions combined with a family…
We consider a variation of $O(N)$-symmetric vector models in which the vector components are Grassmann numbers. We show that these theories generate the same sort of random polymer models as the $O(N)$ vector models and that they lie in the…
We recall the many obstacles which seemed, long ago, to prevent supersymmetry from possibly being a fundamental symmetry of Nature. We also present their solutions, leading to the construction of the supersymmetric extensions of the…
We construct the N=1 supersymmetric extension of double field theory for D=10, including the coupling to an arbitrary number n of abelian vector multiplets. This theory features a local O(1,9+n) x O(1,9) tangent space symmetry under which…
Motivated by the idea of Comprehensive Unification, we consider a gauged $SO(3)$ flavor extension of the Standard Model, including right-handed neutrinos and a Peccei-Quinn symmetry. The model accommodates the observed fermion masses and…
We discuss a special ``symplectic'' class of N = 4 supersymmetric sigma models in (0+1) dimension with 5r bosonic and 4r complex fermionic degrees of freedom. These models can be described off shell by N = 2 superfields (so that only half…
We suggest a mechanism explaining the origin of three generations of the Standard Model fermions from one generation in a higher-dimensional theory. Four-dimensional fermions appear as zero modes trapped in the core of a topological defect…
We study the corrections to $\epsilon^\prime /\epsilon$ in the minimal supersymmetric model at the leading order in QCD and QED. Supersymmetry can increase the standard model prediction for $\epsilon^\prime /\epsilon$ by at most 40\% for…
It is shown that supersymmetric integrable models in two dimensions, both relativistic (i.e. super-Toda type theories) and non-relativistic (reductions of super-KP hierarchies) can be associated to general Poisson-brackets structures given…
The present lectures contain an introduction to possible new physics beyond the Standard Model. Having in mind first of all accelerator experiments of the nearest future we concentrate on supersymmetry, a new symmetry that relates bosons…
Could one use supersymmetry to relate the fermions, constituants of matter, with the bosons messengers of the interactions? This is, ideally, what a symmetry between fermions and bosons would be expected to do. However many obstacles…
I outline a program to derive the Standard Model directly from superstring theory. I present a class of three generation superstring standard--like models in the free fermionic formulation. I discuss some phenomenological properties of…
We present a surprising redefinition of matrix fermions which brings the supercharges of the $\cal N$-extended supersymmetric $A_{n-1}$ Calogero model introduced in [1] to the standard form maximally cubic in the fermions. The complexity of…
In these introductory lectures, we review the theoretical tools used in constructing supersymmetric field theories and their application to physical models. We first introduce the technology of two-component spinors, which is convenient for…
We discuss some testable predictions of a non-supersymmetric $SO(10)$ model supplemented by a Peccei-Quinn symmetry. We utilize a symmetry breaking pattern of $SO(10)$ that yields unification of the Standard Model gauge couplings, with the…
After we study the 6-dimensional ${\cal N} = (1, 1)$ supersymmetry breaking and $R$ symmetry breaking on $M^4\times T^2/Z_n$, we construct two ${\cal N} = (1, 1)$ supersymmetric $E_6$ models on $M^4\times T^2/Z_3$ where $E_6$ is broken down…
We examine the problem of supersymmetry breaking in realistic superstring standard--like models which are constructed in the free fermionic formulation. We impose a supersymmetric vacuum at the Planck scale by requiring vanishing F and D…