Cosmological Vacuum Selection and Meta-Stable Susy Breaking

Ioannis DalianisIFT-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

•

222 ~ TrTrTrK ISS TrhhTrWISS2~

)( cNSU

2/3 cf NN )( cf NNSU

cf NNN

ff NN NN f ~,

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.

hT ssbc /~

~susycT

min min

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 g4 is positive then we have the Kitano Model of gravitationally stabilized gauge mediation.

1st 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

1st Case: Kitano Model: Gravitationally Stabilized Gauge Mediation

1. When g4 is positive then we have the Kitano Model of gravitationally stabilized gauge mediation:

2nd Case - Generalized O’R Models

1. When g4 is positive, then we have the Kitano Model of gravitationally stabilized gauge mediation.

2.When g4 is negative and then we have a supersymmetric breaking minimum which remain in the global-susy limit:

where for vacuum stability:

3rd Case - Generalized O’R Models

1. When g4 is positive, then we have the Kitano Model of gravitationally stabilized gauge mediation.

2.When g4 is negative and then we have a supersymmetric breaking minimum which remain in the global-susy limit:

3. When g4 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)

q

S

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

crT ST

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:

• 1st case:

•2nd case:

•3rd case:

• For all the cases we find that this second critical temperature is always lower than the firstcritical 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

ST

• 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) 1.

2.

3.

•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 fieldsduring 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.