Discrete R Symmetries and Low Energy Supersymmetry

TL;DR

This paper investigates the role of discrete R symmetries in low energy supersymmetry, proposing models that address supersymmetry breaking, the $bla$ problem, and proton decay, with implications for gauge and gravity mediation.

Contribution

It introduces new classes of models with spontaneously broken discrete R symmetries, simplifying metastable supersymmetry breaking and solutions to the $bla$ problem and proton decay.

Findings

Models with discrete R symmetries can naturally break supersymmetry

Retrofitting is effective for gauge mediation and cosmological constant issues

R symmetries help suppress dangerous operators in supersymmetric theories

Abstract

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 supersymmetry breaking. We explain that in gauge mediation, the problem of the cosmological constant makes "retrofitting" particularly natural -- almost imperative. We describe new classes of models, with interesting scales for supersymmetry breaking, and which allow simple solutions of the $\mu$ problem. We argue that models exhibiting such R symmetries can readily solve not only the problem of dimension four operators and proton decay, but also dimension five operators. On the other hand, in theories of "gravity mediation", the breaking of R symmetry is typically of order $M_p$, R parity is required to suppress dimension four $B$ and $L$ violating operators, and dimension five operators remain problematic.