A Scheme for Metastable Supersymmetry Breaking Yutaka Ookouchi ( Perimeter Institute ) Based on : H. Ooguri, Y.O. and C. Park ( 0704.3613 ) J. Marsano, H. Ooguri, Y.O. and C. Park ( 0712.3305 ) R. Kitano and Y.O. ( 0812.0543 ) SUSY BREAKING 09, at IPPP

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

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

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?

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

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

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

The First Example : Seiberg-Witten Theories

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

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

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]

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

subtlety : Higher terns in Kahler Normal Coordinate

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

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!

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

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?

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 &

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

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

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

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

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 ]

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]

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]