Scenarios for SUSY Breaking

The results of the previous sections have shown us that the general results extracted in the past years about gaugino condensation in string models, in terms of the field $S$, are robust. We have seen how gaugino condensation can in principle lift the string vacuum degeneracy and break supersymmetry at low energies (modulo the problems mentioned before). But this is a very particular field theoretical mechanism and it would be surprising that other nonperturbative effects at the Planck scale could be completely irrelevant for these issues. In general we should always consider the two types of nonperturbative effects:stringy (at the Planck scale) and field theoretical (like gaugino condensation). Four different scenarios can be considered depending on which class of mechanism solves each of the two problems: lifting the vacuum degeneracy and breaking supersymmetry.

For breaking supersymmetry at low energies, we expect that a field theoretical effect should be dominant in order to generate the hierarchy of scales (it is hard to believe that a nonperturbative effect at the Planck scale could generate the Weinberg-Salam scale). We are then left with two preferred scenarios: either the dominant nonperturbative effects are field theoretical, solving both problems simultaneously, or there is a `two steps' scenario in which stringy effects dominate to lift vacuum degeneracy and field theory effects dominate to break supersymmetry. The first scenario has been the only one considered so far, it includes gaugino condensation and also the discussion of the previous section in terms of field-dependent soft breaking terms. The main reason this is the only scenario considered so far is that we can control field theoretical nonperturbative effects but not the stringy. In this scenario, independent of the particular mechanism, we have to face the cosmological moduli problem.

In the two steps scenario the dilaton and moduli fields are fixed at high energies with a mass $\sim M_{Planck}$ thus avoiding the cosmological moduli problem. It is also reasonable to expect that Planck scale effects can generate a potential for $S$ and $T$. The problem resides in the implementaion of this scenario [99,75], mainly due to our ignorance of nonperturbative string effects.

In the two steps scenario, after we have fixed the vev of the moduli by stringy effects, it remains the question of how supersymmetry is broken at low energies. Notice that we would be left with the situation present before the advent of string theory in which the gauge coupling is field independent. In that case we know from Witten's index that gaugino condensation cannot break global supersymmetry. Since there are no `moduli' fields with large vev's, the supergravity correction should be negligible because we are working at energies much smaller than $M_{Planck}$.

In fact we can perform a calculation by setting $S$ to a constant in eq. (41), it is straightforward to show that supersymmetry is still unbroken in that case [99], as expected. A more general way to see this is computing explicitly the $1/M_{Planck}$ correction to a global supersymmetric solution $W_\phi=0$, and see that it coincides with the solution of $W_\phi+WK_\phi/M_p^2=0$ which is always a supersymmetric extremum of the supergravity scalar potential.

There seems to be however a counterexample in the literature [74], where supersymmetry was found to be broken with vanishing cosmological constant in supergravity but unbroken in global supersymmetry. Nevertheless it can be seen that in that case, the global limit is such that $K_{UU^*}$ vanishes, and so the kinetic energy for $U$. This makes the corresponding minimum in the global case ill defined, since there may be other nonconstant field configurations with vanishing energy. This is then not a counterexample, because the global theory is not well defined in the minimum.

We are then left with a situation that if global supersymmetry is unbroken, we cannot break local supersymmetry, unless there are moduli like fields. If we insist to have the two steps scenario, this can bring us further back to the past and reconsider models with dynamical breaking of global supersymmetry. These models have attracted recent attention partly due to the better understanding of supersymmetric models from Seiberg and collaborators. Then gravity will no longer be the mediator of supersymmetry breaking.

Independent of string theory we can classify broken supersymmetric models by the mediator of supersymmetry breaking. Currently there are three main scenarios considered: the standard gravity mediated scenario that we have discussed in which the supersymmetry breaking scale is of the order of $10^{11}$ GeV, the gauge mediation scenario [100] in which gauge interactions instead of gravity mediate the breaking of supersymmetry, in this case the scale of breaking has to be close to 1 TeV and more recently, it was discovered a new universal mechanism for communicating the breaking of supersymmetry known as anomaly mediation [101], since the existence of the conformal anomaly is enough to communicate the breaking of supersymmetry to the observable sector. Each scenario has its pros and cons and all are under constant consideration in phenomenological studies. Which scenario will be the dominant in string theory is very model dependent.

Therefore, there is not yet a compelling scenario for supersymmetry breaking and the field remains open, but now we have a much better perspective on the relevant issues. The nonrenormalizable hidden sector models of which the gaugino condensation is a particular case, may need a convincing solution of the cosmological moduli problem to still be considered viable. Hopefully, this will lead to interesting feedback between cosmology and string theory [102]. A good example of this string-cosmology interaction is the recent work by the authors of ref.[103], on which investigations on string cosmology is leading to interesting experimental searches for gravitational waves in ranges not explored before. Furthermore, the recent progress in understanding supersymmetric gauge theories can be of much use for reconsidering gaugino condensation with hidden matter, the discussion in the string literature is far from complete. The understanding of models with chiral matter could also provide new insights to global supersymmetry breaking, relevant to the two steps scenario mentioned above.