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)
quarks, antiquarks (in fundamental-antifundamental representation of SU(N)
mesons (gauge singlets)
ISS Model
K ISS
2
2
 Tr   Tr ~  Tr 
2
WISS  hTr ~   h 2Tr
• It is a magnetic dual theory of SUSY-QCD with gauge group SU ( N c )
• When N f  3N c / 2 the electric theory is asymptotically free whereas its dual, with
gauge group SU ( N f  N c ) is infrared free.
• N  N f  N c is the magnetic number of colours
•   N f  N f matrix,
 , ~  N f  N matrices
• It has susy breaking solutions, generated by non-vanishing F-terms for the mesons
•
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 Tcssb ~  / h there is a second order phase transition to the
no susy vacuum (which is temporally global minimum)
3) At temperature Tcsusy ~  the two minima are degenerated.


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):
Singlet chiral superfield
messenger fields,
carry SM quantum numbers
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:
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
minimum:
then we have a supersymmetric breaking
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)
S
q
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
Tcr
TS
Finite Temperature Corrections
(The system in the Radiation Dominated Early Universe )
The second critical temperature TS 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 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)
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 nonsupersymmetric 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.