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Context: 2024 evidence of positive cosmological constant, lack of supersymmetry evidences, value of ~meV for the energy scale of the observed cosmological constant.

Is a positive cosmological constant a hint that superstrings, supergravity, ...at least as we thought they should be, are wrong? After all:

  1. The world does not seem to be supersymmetric at about meV energy scale.
  2. It seems weird that SUSY would be broken in such a way (fine-tuning) to be left only with such tiny value.
  3. Known SM particles are not enough (even if we found new particles to explain DM or DE we have not guarantee they will match bosonic and fermionic degrees of freedom, and even worst, we should imagine a way to break SUSY so we had a small CC at low energies; it is not impossible but it points out to anthropic principles or the Multiverse).
  4. After the discovery of cosmic positive acceleration, and so a positive cosmological constant, SUSY theoretical motivation of having a cero cosmological constant was lost. Thus, SUSY must be broken at $M<M_P$ to get the right cosmological constant value.

In summary, what are the reasons to believe, yet, in SUSY (SUGRA, superstrings,...) at high energies (e.g., Planck or intermediate scales) today if we accept the value of the cosmological constant we have today?

riemannium
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1 Answers1

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The cosmological constant does not provide motivation for supersymmetry.

People study supersymmetry for reasons ranging from theoretical -- e.g., the extra symmetry allows certain non-perturbative calculations to be done, superstring theory unifies gravity and quantum mechanics and naturally contains supersymmetry -- to phenomenological -- potentially providing an explanation for the hierarchy problem and giving a dark matter candidate (although the parameter space for both of these scenarios has shrunk over the past decade or so), makes the Standard Model coupling constants meet at a single scale (GUT scale), and it is a logical possibility for what kinds of particles might exist so it's worth exploring the consequences.

The cosmological constant can be incorporated into supersymmetry, by having a vacuum where supersymmetry is spontaneously broken, and having some non-supersymmetric mechanism to explain the cosmological constant problem (like the anthropic principle). So, the cosmological constant doesn't rule out supersymmetry.

But, you are right that there is some tension there. The hierarchy problem and cosmological constant problem are both the same kind of fine tuning problem, but we can only plausibly use supersymmetry to explain the hierarchy problem, because we know from experience that the vacuum cannot be supersymmetric at the energy scale of the cosmological constant. (And a supersymmetric vacuum must have a vanishing cosmological constant).

Summarizing, I think there are roughly two schools of thought for why people study supersymmetry despite supersymmetry not being able to directly address the cosmological constant problem. One would be that supersymmetry is a useful mathematical tool for studying quantum field theories, and whether or not it is realized in Nature is beside the point. Two would be that supersymmetry could still be realized in Nature at high energies, and it naturally connects with other ideas in high energy physics, and whatever physics is relevant for the cosmological constant problem is just not directly related to supersymmetry.

Andrew
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