Realistic Type I,II Brane Models with Broken SUSY

After the introduction of D-branes, the perspective about type I models has changed completely. It allows us to look for the standard model not only inside the `bulk' 10-dimensional spacetime but also inside some of the lower dimensional D-branes that appear in such vacua. Much work has been devoted recently to the construction of 4-dimensional type I models. A particularly useful way to build open type I string models is to start with closed type IIB strings and perform a kind of orbifold twist on the (2-dimensional) string worldsheet identifying the two orientations of type IIB strings, this is called an `orientifold'. On top of this, compactifications similar to those of the heterotic string in terms of orbifolds have been obtained, classified by the different twists and background gauge fields or Wilson lines. The net result of this investigation is that although similar to the heterotic strings, many chiral models can be constructed preserving $N=1$ supersymmetry, none of them can be claimed to be close to the Standard Model. One of the reasons for this lack of realistic models is the fact that there are consistency conditions that the models have to satisfy in order to avoid unwanted tadpoles (which if existing would give rise to anomalies in the 4-dimensional theory). These tadpole cancellation conditions happen to be more restrictive than the corresponding conditions in the heterotic case and therefore there is less room for realistic models. In order to obtain realistic models we may relax the conditions we had imposed on the models, in particular we may look for models without supersymmetry. Notice that this possibility was not open to us in the heterotic case because constructing a nonsupersymmetric model at the Planck scale would leave us without a solution to the hierarchy problem. As argued in the previous section, in type I models we may have the string scale lower than $10^{12}$ GeV. In this case having a nonsupersymmetric model may still solve the hierarchy problem at low energies as long as we have gravity mediated supersymmetry breaking in the visible sector of scenario 3. above, for which the splitting in multilplets will be of the order $M^2/M_{Planck}\leq 1$ TeV. On scenario 4. we may just have explicit supersymmetry breaking without any danger. Therefore in nonsupersymmetric brane models are now an interesting alternative to the supersymmetric string vacua. A concrete way to build nonsupersymmetric brane models is to look for string vacua including both branes and antibranes. It is known that a brane, being a BPS state, breaks partially supersymmetry, an anti-brane breaks the remaining supersymmetry so the configuration brane/anti-brane is non supersymmetric. However brane/anti-brane configurations tend to be unstable which usually shows in the appearance of tachyons in the spectrum. In orbifolds of type I models this can be avoided by having the antibranes of different dimension than the branes which then do not annihilate each other. Furthermore, tadpole cancellation conditions force some of the branes or anti-branes to be trapped in some of the orbifold fixed points avoiding the annihilation of branes and anti-branes of the same dimensionality. We can then envisage models with, for instance, D7-branes with D3-branes trapped at some of the orbifold fixed points and some anti D3-branes trapped at different orbifold singularities which cannot annihilate each other. Models of this type have been explicitly constructed recently [116,117] with the following physical properties:

1. On the D7-branes there is the gauge symmetry $SU(3)_c\times SU(2)_L\times U(1)_Y$ or its left-right extension $SU(3)_c\times SU(2)_L\times SU(2)_R\times U(1)_{B-L}$ the matter sector includes three families of quarks and Higgs fields.
2. On the trapped D3-branes and anti D3-branes there are extra gauge fields which for the D3 case are broken by some flat directions in the model. The three families of lepton fields appear as open strings with one endpoint on a D3-brane and the other on the D7-brane.
3. The presence of `hidden' anti-D3-branes explicitly break supersymmetry, but its breaking is felt by the visible sector only through gravitational strength interactions. Therefore if the string scale is the intermediate scale this would correspond to the gravity mediated supersymmetry breaking scenario. If the anti-D3 branes happen to be inside the D7-branes then the breaking of supersymmetry is explicit and a TeV fundamental scale is required.
4. The D-brane origin of the $U(1)$ gauge groups fixes the hypercharge normalization to be $3/14$ different from the $3/8$ of $SO(10)$ GUTs. Furthermore the appearance of three rather than one families of Higgs fields change the RG running of the couplings in such a way that unification occurs at the intermediate scale $M\sim 10^{11}$ GeV. This is particularly realised in the left-right models for the scale of $SU(2)_R$ breaking close to 1TeV, having then important experimental consequences at present and future collider. The 1TeV scenario fails to satisfy the gauge coupling unification in this class of models.
5. Yukawa couplings providing structure of quarks and lepton masses (including neutrino masses) can be obtained from the the superpotential. Their full understanding requires also knowledge of the Kahler potential which is not under complete control.
6. The particular way that the three lepton families are distributed among the branes gives rise to discrete versions of lepton number as exact symmetry of the models. Further discrete symmetries obtained from the structure of the original flat directions, give rise naturally to $R$-parity as an exact discrete symmetry forbidding fast proton decay.
7. There are particular (Ramond-Ramond) axion fields at the singularities with the properties and couplings needed to solve the strong CP problem. This depends crucially on the fact that the fundamental scale is intermediate. This was not possible in the old heterotic models.
8. The explicit potential for the scalar fields is not known and the minimisation process cannot be performed at present. It is yet to be seen that this stabilisation could fix the value of the compact space to the `right value' as to obtain the intermediate fundamental scale and the even most difficult requirement of generating a very small cosmological constant which is not protected after supersymmetry was broken. These are left as open questions for the moment.

Finally we have recently found that this class of type I models is contained in a more general class of models constructed directly from type IIB strings. In this case we can concentrate in type IIB models and follow a bottom-up approach looking for explicit D3-brane worlds located at singularities of the 10-dimensional space. We find remarkably simple realistic three-generation models similar to the ones above. Many of the features of these models are local, i.e., depending only on the singularity structure and not on the particular compactification (if any). The stability of the brane/anti-brane system can be better controlled in these constructions and some phenomenological issues, such as the structure of fermion masses, look more promising than the related type I models. If the construction involves the orientifold twist we recover the (T-duals of) the type I models with the standard model fields living on D3-branes[118].