The idea of breaking supersymmetry in a dynamical way was first presented in refs. [71]. In those articles a general topological argument was developed in terms of the Witten index , showing that dynamical supersymmetry breaking cannot be achieved unless there is chiral matter or we include supergravity effects for which the index argument does not apply. This was subsequently verified by explicitly studying gaugino condensation in pure supersymmetric YangMills, a vectorlike theory, for which gauginos condense but do not break global supersymmetry [72] (for a review see [73]). Breaking global supersymmetry with chiral matter was an open possibility in principle, but this approach ran into many problems when tried to be realized in practice.
The situation improved very much with the coupling to supergravity. The reason was that simple gaugino condensation was argued to be sufficient to break supersymmetry once the coupling to gravity was included. This works in a hidden sector mechanism where gravity is the messenger of supersymmetry breaking to the observable sector [74]. However, it has recently been realized that the proposal in [74] does not work (see for instance [75] which also includes an extended discussion of the current status of gaugino condensation); coupling with supergravity does not actually change the situation in global supersymmetry where gaugino condensation does not break supersymmetry. The missing ingredient was the fact that gauge couplings were considered to be constant rather than field dependent. Gaugino condensation with field dependent gauge couplings was anticipated in ref. [76] and is realized in a very natural way in string theory. As we have seen, the gauge coupling is a function of the dilaton and moduli fields. Furthermore, string theory provides a natural realization of the hidden sector models [77,78] by having a hidden sector especially in the versions.
To study the effects of gaugino condensation we should be able to answer the following questions: Do gauginos condense? If so, is supersymmetry broken by this effect? What is the effective theory below the scale of condensation? In order to answer these questions, several ideas have been put forward [72,76,78,79,80,81]. The most convenient formalism is in terms of the socalled 2PI effective action [81]. In order to understand this formalism, it is convenient to think about the case of spontaneous breaking of gauge symmetries. In that case we minimize the effective potential for a Higgs field, obtained from the 1PI effective action and see if the minimum breaks or not the corresponding gauge symmetry. In our case, we are interested in the expectation value of a composite field, namely or its supersymmetric expression . Therefore we need the two particle irreducible effective action (2PI).
We start then with the generating functional in
the presence of an external current coupled to
the operator that we want the expectation value of,
namely,
. Let us consider the simplest case of a single
hidden sector gauge group in global supersymmetry.
(Coupling to supergravity presents no obstacles but
make the discussion more cumbersome [81,75].)
(37) 
(38) 
(39) 
(40) 
(41) 
By studying the effective potential for we recover the previously known results. For one condensate and field independent gauge couplings (no field ) the gauginos condense () but supersymmetry is unbroken. For field dependendt gauge coupling, the minimum is for ( ) so gauginos do not condense (this is reflected in the runaway behaviour of the Wilsonian action for ).
Alternatively, after eliminating from its field equations and using (42), we find the scalar potential for the real parts of and ( and respectively), namely . This potential has a runaway behaviour for both and , as expected.
The dependence of the potential was completely changed after the consideration of target space or duality. It was shown [82], that imposing this symmetry
changes the structure of the scalar potential for the moduli fields
in such a way that it develops a minimum at (in
string units), whereas the potential blowsup at the decompactification
limit (
), as desired (see figure 3)
^{}.
The modifications due to imposing duality can be traced to the fact
that the gauge couplings get moduli dependent threshold corrections from
loops of heavy string states [83] as in eq. (29). This in turn generates a
moduli dependence on the superpotential induced by gaugino condensation
of the form
(43) 

This mechanism however did not help in changing the runaway behaviour of the potential in the direction of . There is a very generic problem emphasized mostly by Dine and Seiberg [84] . It is known that because at large the string is weakly coupled, the potential has to vanish asymptotically (towards a free theory). Any other minimum has to be at strong coupling for which the perturbation expansion does not work, unless there is an extra parameter that could be tuned. Such a mechanism was proposed in [85]. For stabilizing , the proposal was to consider gaugino condensation of a nonsemisimple gauge group, inducing a sum of exponentials in the superpotential which can conspire to generate a local minimum for [85]. The role of the extra parameter can be played by the ratio of beta function coefficients of the different groups. These have been named `racetrack' models in the recent literature.
It was later found that combining the previous ideas, together with the addition of matter fields in the hidden sector (natural in many string models)[86,87], was sufficient to find a minimum with almost all the right properties, namely, and fixed at the desired value, , supersymmetry broken at a small scale ( GeV) in the observable sector, etc. This lead to studies of the induced soft breaking terms at low energies. Besides that relative success there are several problems that assure us that we are far from a satisfactory description of these issues.
Another important puzzle was: we know that the field only appears after performing a duality transformation changing the stringy field to the axion . A nontrivial potential for gives a mass to and then it is no longer dual to ! This puzzle was recently solved [81] by analyzing gaugino condensation directly in the version. The end result was that dissapears from the lowenergy spectrum and a massive field takes its place, having one propagating degree of freedom and being dual to a massive axion .