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

If nature exhibits low energy supersymmetry, discrete (non-$Z_2$) R symmetries may well play an important role. In this paper, we explore such symmetries. We generalize gaugino condensation, constructing large classes of models which are classically scale invariant, and which spontaneously break discrete R symmetries (but not supersymmetry). The order parameters for the breaking include chiral singlets. These simplify construction of models with metastable dynamical supersymm...

A global symmetry of a quantum field theory is said to have an 't Hooft anomaly if it cannot be promoted to a local symmetry of a gauged theory. In this paper, we show that the anomaly is also an obstruction to defining symmetric boundary conditions. This applies to Lorentz symmetries with gravitational anomalies as well. For theories with perturbative anomalies, we demonstrate the obstruction by analyzing the Wess-Zumino consistency conditions and current Ward identities in ...

Discrete R symmetries are interesting from a variety of points of view. They raise the specter, however, of domain walls, which may be cosmologically problematic. In this note, we describe some of the issues. In many schemes for supersymmetry breaking, as we explain, satisfying familiar constraints such as suppression of gravitino production, insures that the domain walls are readily inflated away. However, in others, they form after inflation. In these cases, it is necessary...

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 investigate non-Abelian R-symmetries in $\mathcal{N}=1$ supersymmetric theory, where fields may transform under the R-symmetry in representations with dimension higher than one. While a continuous non-Abelian R-symmetry can always be decomposed to a $U(1)$ R-symmetry and non-R symmetries, there are non-trivial discrete non-Abelian R-symmetries that do not admit such a decomposition, and effective R-charges cannot be defined in such models. Previous results on sufficient co...

We discuss local \R-symmetry as a potentially powerful new model building tool. We first review and clarify that a $U(1)$ \R-symmetry can only be gauged in local and not in global supersymmetry. We determine the anomaly-cancellation conditions for the gauged \R-symmetry. For the standard superpotential these equations have {\it no} solution, independently of how many Standard Model singlets are added to the model. There is also no solution when we increase the number of famil...

This talk summarizes our recent work establishing an algebraic, model-independent basis for the existence of \B bounds and \B equations for topologically non-trivial solitons and instantons. Our arguments use supersymmetry in an essential way to understand both supersymmetric and non-supersymmetric theories. Our arguments are constructive and work in nearly any number of dimensions. Presented at and to appear in the proceedings of the XX^{th} International Colloquium on Group...

We make a comprehensive study of the theory and phenomenology of a low energy supersymmetric standard model originating from a string-inspired $E_6$ grand unified gauge group. The Exceptional Supersymmetric Standard Model (ESSM) considered here is based on the low energy SM gauge group together with an extra $Z'$ corresponding to an extra $U(1)_{N}$ gauge symmetry under which right--handed neutrinos have zero charge. The low energy matter content of the ESSM corresponds to th...

We comment on aspects of discrete anomaly conditions focussing particularly on $R$ symmetries. We review the Green-Schwarz cancellation of discrete anomalies, providing a heuristic explanation why, in the heterotic string, only the "model-independent dilaton" transforms non-linearly under discrete symmetries; this argument suggests that, in other theories, multiple fields might play a role in anomaly cancellations, further weakening any anomaly constraints at low energies. We...

We discuss consistency at the quantum level in the rigid $\mathcal N=1$ supersymmetric field theories with a $U(1)_R$ symmetry in four-dimensional curved space which are formulated via coupling to the new-minimal supergravity background fields. By analyzing correlation functions of the current operators in the $\mathcal{R}$-multiplet, we show that the quantum consistency with the (unbroken) supersymmetry requires the $U(1)_R$ anomaly coefficient, which depends only on the fie...