# Exploring R Symmetry in SUSY

• BenTheMan
In summary, the conversation discusses the concepts of R symmetry and R-parity in relation to N=1 supersymmetry. R symmetry is a global U(1) symmetry that can be spontaneously broken and is necessary for supersymmetry breaking. R-parity, on the other hand, is a discrete symmetry that distinguishes between ordinary particles and superparticles. The conversation also mentions the importance of R symmetry in probing nonperturbative effects and its relationship with the Witten index.

#### BenTheMan

Is there a nice, cute way to see what R symmetry is? I mean, N=1 SUSY has a global $$U(1)_R$$ symmetry, which is a charge carried by the supercharges, right? And a spontnaeously broken $$U(1)_R$$ is a sufficient (but not necessary) condition for broken global SUSY. (Counter-example is O'Raifeartaigh type models with broken SUSY but an intact $$U(1)_R$$.)

Is there anything else that I'm missing, or have I screwed something up?

I'm not sure. I memorized that R-parity odd particles(Pr=-1) are sparticles and R-parity even particles (Pr=+1) are ordinary particles.
Do you mean a model while you'r saying "a cute way" ??

Well, R-symmetry and R-parity are two different things, that are only sometimes related.

I think I just need to read some more of Seiberg's papers. I think he has a set of lecture notes where he outlines this in some more detail.

Could you post references to the Seiberg papers you refere to?

R Symmetries is basically an invariance of a supersymmetry algebra free of central charges under a group U(N) of internal symmetries. So for N=1 SuSy you have a U(1) invariance. This implies that in the lagrangian the left and right handed parts of the gaugino fields will have invariant transformations by phases (the left will transform with a negative phase and the right with a positive phase)

This symmetry can be spontaneously broken or violated by anomalies, and so forth depending on the specifics of the theory. There are interesting relationships with things like the Witten index, and this symmetry is important in probing interesting nonperturbative effects. Also the existence of R symmetry is a necessary condition for SuSy breaking.

But what you wrote also sounds right. A spontaneously broken R symmetry is a sufficient condition for Susy breaking at least for most generic classes.

## 1. What is R-symmetry in SUSY?

R-symmetry is a mathematical symmetry in supersymmetric (SUSY) theories that relates particles with different spin. It is a global symmetry that is used to classify particles and their interactions. In SUSY, R-symmetry is related to the conservation of a quantum number called R-parity, which helps to explain the stability of the proton and the existence of dark matter.

## 2. How is R-symmetry explored in SUSY?

R-symmetry is explored in SUSY through theoretical and experimental studies. Theoretical studies involve developing mathematical models and equations that describe the properties and behavior of particles in SUSY with R-symmetry. Experimental studies involve using particle accelerators and detectors to observe and measure the properties of particles in SUSY and test the predictions made by theoretical models.

## 3. What are the implications of R-symmetry in SUSY?

R-symmetry in SUSY has several implications, including the conservation of R-parity, which can impact the stability of the proton and the existence of dark matter. R-symmetry also plays a role in the hierarchy problem, which refers to the large difference in the mass scales of the subatomic particles. Additionally, R-symmetry can help to explain the origin of matter-antimatter asymmetry in the universe.

## 4. Are there any experimental evidence for R-symmetry in SUSY?

Currently, there is no direct experimental evidence for R-symmetry in SUSY. However, several experiments, such as the Large Hadron Collider (LHC) at CERN, are actively searching for particles predicted by SUSY with R-symmetry. These experiments may provide evidence for R-symmetry in the future.

## 5. How does R-symmetry affect the search for new physics beyond the Standard Model?

R-symmetry is one of the fundamental principles that guide the search for new physics beyond the Standard Model. It is used to develop and test new theories and models that can explain the limitations of the Standard Model, such as the hierarchy problem and the unification of fundamental forces. R-symmetry also helps to guide the design and interpretation of experiments that search for new particles and interactions beyond the Standard Model.