1. A Scheme for Metastable Supersymmetry Breaking
Yutaka Ookouchi ( Perimeter Institute )
Based on :
H. Ooguri, Y.O. and C. Park ( )
J. Marsano, H. Ooguri, Y.O. and C. Park ( )
R. Kitano and Y.O. ( )
SUSY BREAKING 09, at IPPP

2. Claim and Plan of Talk
A relatively simple method to create a metastable state
Applicable to a wide class of theories
General argument
Seiberg-Witten Theories
Generalized Wess-Zumino Models
Phenomenologicaly viable possibility

3. A Scheme for Metastable state
For simplicity let me focus on model with one chiral superfield
This never have a metastable state because of holomorphy.
We need a non-trivial Kahler metric

4. Question is
For a model with given metric , consider superpotential deformation
At the leading order, back reaction to metric is negligible
[ Intriligator-Seiberg-Shih `06]
What is a condition for to create a metastable state?

5. Kahler Normal Coordinate
Stability is a local structure. So it is convenient to use the normal coordinate
[Alvares-Gaume, et al. `81] [Higashijima-Nitta `00 ]
In the coordinate, expansion coefficients of Kahler potential are all covariant quantities.
At the cubic order the normal coordinate is

6. CLAIM: Use the normal coordinate for W
The potential is
Positive if
Positive

7. Longevity and Stability
A dimensionful parameter in the given metric
Distance :
Height :
Decay probability is small
when
How much do we have to tune parameters?
Need tuning of order scalar curvature

8. The First Example :
Seiberg-Witten Theories

9. Review of Seiberg-Witten Theories
N=2 Supersymmetric gauge theory with group G
Low energy effective theory on Coulomb branch is
theory described by the prepotential

10. Proof of the negativity
For Kahler manifold
In Seiberg-Witten theory (use “a” as a local coordinate X)
Everywhere
(except singular points)
We can make a metastable state anywhere in moduli space by our method

11. SU(2) Seiberg-Witten theory
Using the normal coordinate at the origin
At the low energy
Im[u]
The potential has four unlifted SUSY preserving vacua
Re[u]

12. Metastable vacuum at the origin
Re[u]
Im[u]
Re[u]
Re[u]

13. subtlety :
Higher terns in Kahler Normal Coordinate

14. However it is important for SUSY breaking in N=2 model
Until now we have ignored higher terms of normal coordinate because they do not affect stability
However it is important for SUSY breaking in N=2 model
In Seiberg-Witten theory

15. All order KNC is an electric/magnetic FI-term!
But.. Why? We have no idea. Any reason?
This equivalence is surprising. Because it means that the
hidden SUSY is preserved on the vacuum!

16. Quick explanation : SUSY tr. of fermions
[ Antoniadis-Partouche-Taylor `96]
[ Aganagic-Beem-Seo-Vafa ‘07]
Original N =2 SUSY
Manifest SUSY
Hidden SUSY

17. Puzzle ? Earlier we saw an example for SUSY breaking
But now we understand that inclusion of all order term preserves ``hidden” SUSY
How do we reconcile two things?

18. Answer: Global Structure
Higher terms change the Global structure
Truncation of normal coordinate breaks the hidden SUSY in the higher interaction terms
SU(2) SW theory
Truncated
All Order
Singular Kahler
Singular Kahler &

19. The Second Example :
Wess-Zumino Models
--Direct Gauge Mediation Model--

20. Consider a generalized WZ-model:
Canonical Kahler potential
Renormalizable model
can be messengers
We are interested in large X regime
can be integrated out

21. Loop corrections generate nontrivial metric to the X
One loop factor
Plugging into the definition of curvature
We get two interesting cases:

22. One Loop correction generates
[ Grisaru-Rocek-von Unge `96]
Appropriate choice of we can get a point where
In this case, by normal coordinate we can create a metastable vacua at

23. Two loop corrections needed
Two loop corrections needed. For simplicity we focus on minimal matter content
Coefficients are given by discontinuity of anomalous dimension at the threshold
[ Giveon-Katz-Komargodski-Shih`08 ]
[ Intriligator-Shih-Sudano `08 ]

24. Explicit computation shows
Everywhere
So we can create a metastable vacuum anywhere in large X region by our method
It is interesting to identify as messengers
Turning off the messenger interaction destabilize the
vacuum
So this model fits into the definition of direct gauge
mediation
Direct Gauge Mediation
[ Dine-Mason `07]
[ Carpenter-Dine-Festuccia-Mason `08]

25. Summary Quite general method for creating a metastable state
Applicable to All Seiberg-Witten theories and various
generalized WZ models
Generaliztion to d<4 theories can be possible
Simple renormalizable direct gauge mediation models
Need UV completion and Retrofitting
[ Dine-Feng-Silverstein `06]