Note on gauge and gravitational anomalies of discrete $Z_N$ symmetries

I provide a pedagogical introduction to supersymmetry. The level of discussion is aimed at readers who are familiar with the Standard Model and quantum field theory, but who have had little or no prior exposure to supersymmetry. Topics covered include: motivations for supersymmetry, the construction of supersymmetric Lagrangians, superspace and superfields, soft supersymmetry-breaking interactions, the Minimal Supersymmetric Standard Model (MSSM), R-parity and its consequence...

The role of instantons in describing non-perturbative aspects of globally supersymmetric gauge theories is reviewed. The cases of theories with N=1, N=2 and N=4 supersymmetry are discussed. Special attention is devoted to the intriguing relation between instanton solutions in field theory and branes in string theory.

A fairly non-technical introduction to and survey of supersymmetry phenomenology with pedagogical emphasis, including exercises. Suitable for both theorists and experimentalists. The manuscript appeared as a Springer-Verlag monograph in physics. The body of the manuscript is provided here with the publisher`s permission.

R-symmetry gauged 6D (1,0) supergravities free from all local anomalies, with gauge groups $G\times G_R$ where $G_R$ is the R-symmetry group and $G$ is semisimple with rank greater than one, and which have no hypermultiplet singlets, are extremely rare. There are three such models known in which the gauge symmetry group is $G_1\times G_2 \times U(1)_R$ where the first two factors are $ \left(E_6/{\mathbb{Z}_3}\right) \times E_7$, $ G_2 \times E_7 $ and $F_4 \times Sp(9)$. The...

An introduction to and a partial review of supergravity theories is given, insisting on concepts and on some important technical aspects. Topics covered include elements of global supersymmetry, a derivation of the simplest N=1 supergravity theory, a discussion of N=1 matter-supergravity couplings, of the scalar sector and of some simple models. Space-time is four-dimensional.

Krauss and Wilczek have shown that an unbroken discrete gauge symmetry is respected by gravitationally mediated processes. This has led to a search for such a symmetry compatible with the standard model or MSSM that would protect protons from gravitationally mediated decay in a universe with a low scale for quantum gravity (large extra dimensions). The fact that the discrete symmetry must remain unbroken and have a gauge origin puts important restrictions on the space of poss...

In the minimal supersymmetric standard model, the existence of R-parity is not required for the internal consistency of the theory and might therefore be regarded as ad hoc. I catalog some simple conditions which are sufficient to guarantee that R-parity survives as an unbroken gauged discrete subgroup of the continuous gauge symmetry in certain extensions of the minimal supersymmetric standard model. If these criteria are met, R-parity is automatic. [Based on a talk given at...

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 seemed, long ago, to prevent supersymmetry from possibly being a fundamental symmetry of Nature. Which fermions and bosons could be related? Is spontaneous supersymmetry breaking possible at all? If yes, where is the corresponding spin-1/2 Gold...

We discuss two independent issues about the baryon asymmetry of the universe. First, assuming that it is generated by an unspecified source at high temperatures, we study the effects of non-perturbative $SU(2)_W$ dynamics above the electroweak scale, in the context of supersymmetric models. We find that there is a substantial difference with the nonsupersymmetric case with the net effect of relaxing previous bounds on B and L violating interactions. In particular supersymmetr...

We determine the anomaly free discrete R symmetries, consistent with the MSSM, that commute with SU(5) and suppress the $\mu$ parameter and nucleon decay. We show that the order M of such $Z_M^R$ symmetries has to divide 24 and identify 5 viable symmetries. The simplest possibility is a $Z_4^R$ symmetry which commutes with SO(10). We present a string-derived model with this $Z_4^R$ symmetry and the exact MSSM spectrum below the GUT scale; in this model $Z_4^R$ originates from...