Cosmological Vacuum Selection and Meta-Stable Susy Breaking Ioannis Dalianis IFT-University of Warsaw

Outline Metastable Supersymmetry Breaking - ISS model Metastable Susy Breaking in Generalized O’R models coupled to gravity - Kitano Model Temperature Corrections Cosmological Considerations

Susy Breaking in Meta-stable Vacua N=1 susy gauge theories with massive, vector-like matter have susy vacua (non-zero Witten index) (Witten -‘82) Theories with no-supersymmetric vacua (global minimum no-susy) and dynamically break susy look rather complicated. It has been proposed that susy breaking in meta-stable vacuum is an interesting example of model building (Intriligator, Seiberg, Shih -‘06) These vauca have parametrically long lifetimes, thus protected by tunneling and are phenomenologically viable candidates for susy breaking Classic constraints, needed for having no-susy vacua, don’t constrain models of meta-stable susy breaking Even simple models exhibit the existance of meta-stable vacua, so it is believed to be a generic feature of susy theories. R-symmetry must be approximate (Nelson, Seiberg -‘94) Meta-stable susy breaking seems inevitable (Intriligator, Seiberg, Shih -‘07)

ISS Model It is a magnetic dual theory of SUSY-QCD with gauge group When the electric theory is asymptotically free whereas its dual, with gauge group is infrared free. is the magnetic number of colours matrix, matrices It has susy breaking solutions, generated by non-vanishing F-terms for the mesons quarks, antiquarks (in fundamental-antifundamental representation of SU(N) mesons (gauge singlets)

Finite Temperature Corrections to ISS Model At high temperatures the local susy breaking minimum is typically in a different place from the low temperature minima As the universe cools the system may evolve towards either the susy breaking or susy preserving minima It is found (Craig et al. ’06, Fischler et al. ’07, Abel ‘07) that 1) At high temperatures the minimum is at the origin 2) At temperature there is a second order phase transition to the no susy vacuum (which is temporally global minimum) 3) At temperature the two minima are degenerated.

Generalized O’Raifeartaigh Models (see e.g. Lalak, Pokorski, Turzynski ‘08) We assume that at tree level the fields have canonical Kahler potential and that their interactions are described by the most general superpotential consistent with the R-symmetry The interactions of S with φ fields induce a correction to the effective potential for S which can be approximately accounted for by introducing a correction to the Kahler This correction to the Kahler can be expanded in powers of S Integrating out the heavy chiral superfields φ we end up with a low enegy superpotential. The integrated out heavy fields appear in the low energy theory via the effective Kahler potential.

Generalized O’Raifeartaigh Models Including gravity and messengers the low energy superpotential can be written and the generalized Kahler The supergravity potential is And for real field values we take

Generalized O’R Models – Cases 1. When g 4 is positive then we have the Kitano Model of gravitationally stabilized gauge mediation.

1 st Case: Kitano Model: Gravitationally Stabilized Gauge Mediation The theory (R. Kitano’06): Without Gravity If we neglect the messenger sector this model breaks susy and the S field is stabilized at the origin S=0. Introducing the messenger sector we have susy restoration. There is a supersymmetric minimum at Including Gravity A susy minimum is found: And a no susy minimum: Singlet chiral superfield messenger fields, carry SM quantum numbers

1 st Case: Kitano Model: Gravitationally Stabilized Gauge Mediation 1. When g 4 is positive then we have the Kitano Model of gravitationally stabilized gauge mediation:

2 nd Case - Generalized O’R Models 1. When g 4 is positive, then we have the Kitano Model of gravitationally stabilized gauge mediation. 2.When g 4 is negative and then we have a supersymmetric breaking minimum which remain in the global-susy limit: where for vacuum stability:

3 rd Case - Generalized O’R Models 1. When g 4 is positive, then we have the Kitano Model of gravitationally stabilized gauge mediation. 2.When g 4 is negative and then we have a supersymmetric breaking minimum which remain in the global-susy limit: 3. When g 4 is negative and then we have a supersymmetric breaking minimum: and the stability of this vacuum in the q-direction implies:

Finite Temperature Corrections (The system in the Radiation Dominated Early Universe ) First Step: Tree level (zero temperature) potential. Second step: We write the potential as function of the finite temperature excitations about the thermal average. Third step: We compute the mass matrix about the thermal average values. The temperature corrections are found by the formula:

Finite Temperature Corrections (The system in the Radiation Dominated Early Universe ) The thermally corrected potential, e.g, for the first case (Kitano model) reads: It has a high temperature minimum almost at the origin (for the 3 cases)

Finite Temperature Corrections (The system in the Radiation Dominated Early Universe ) There is a critical temperature at which the system evolves towards the susy preserving vacuum (for the 3 cases): At this temperature the minimum moves from the origin to

Finite Temperature Corrections (The system in the Radiation Dominated Early Universe ) The second critical temperature at which the susy breaking minima are formed depends on the case. For each case we have: 1 st case: 2 nd case: 3 rd case: For all the cases we find that this second critical temperature is always lower than the first critical temperature which drives the system to the susy minima. The study of the evolution of the fields in a phase of high temperature thermal equilibrium disfavors these models of meta-stable susy breaking

Non adiabatic Initial conditions? Scalar Initial VEVs?

Conditions for Selection of the No Susy Meta-stable Vacua in the Early Universe The already presented analysis was based on the assumption that the universe started from radiation dominated phase of thermal equilibrium. However, it is widely believed that the early universe has undergone a non-adiabatic phase: inflation It is plausible and to assume that the fields initially were not placed at the origin of field space but were arbitrary displaced. Actually, the initial conditions for scalar fields are controversial. The conditions are: A) B)

Conditions for Selection of the No Susy Meta-stable Vacua in the Early Universe For the first case (Kitano Model): A comment is that a region of mixed gauge gravity meta-stable susy breaking mediation effect is cosmologically possible.

Conditions for Selection of the No Susy Meta-stable Vacua in the Early Universe For the second case (Global susy breaking minima): And for the third case

Conclusions We have analyzed cosmological vacuum selection in models of gauge mediation and stabilization of the Polonyi field via corrections to the Kahler. We have found that it is the supersymmetric vacua which are naturally selected by the thermal evolution if the initial state at high temperature is close to the origin of the field space The only natural and rather efficient mechanism leading to the non- supersymmetric minimum at low energies is a non-adiabatic displacement of the initial conditions away from the origin A sufficient displacement can be due to the quantum fluctuations of the fields during inflation. The system can land to the no-susy vacua, but still we must talk about a probability, since the field starts oscillations roughly at the time of its decay.