supersymmetry breaking ,r-symmetry breaking ,and metastable vacua in supergravity
DESCRIPTION
Yuji Omura (Kyoto Univ.) Hiroyuki Abe ( YITP,Kyoto Univ.) Tatsuo Kobayashi(Kyoto Univ.). Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity. Supersymmetry (SUSY) is one of the key ingredients - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/1.jpg)
SUPERSYMMETRY BREAKING ,R-SYMMETRY BREAKING ,AND METASTABLE VACUA IN SUPERGRAVITY
Yuji Omura (Kyoto Univ.)Hiroyuki Abe (YITP,Kyoto Univ.)Tatsuo Kobayashi(Kyoto Univ.)
![Page 2: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/2.jpg)
INTRODUCTION Supersymmetry(SUSY) is one of the key ingredientsto study physics beyond the SM :the hierarchy
between the Planck scale and the weak scale , dark matters , and etc……
On the other hand ,SUSY must be broken. Nelson and Seiberg showed “Generally there is broken SUSY if there is an R-symmetry.”
We discuss SUSY Models with a global U(1)R symmetry.
![Page 3: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/3.jpg)
THE SUSY MODELS WITH U(1)R SYMMETRY
U(1)R symmetry must be broken to make nonvanishing Majorana gaugino masses .
Nelson and Seiberg’s argument in global SUSY is
But spontaneous R symmetry breaking causes massless Goldstone boson ,R-axion.
SUSY breaking vacuum is metastable in O’Raifeartaigh Model.
R-symmetry breaking SUSY breaking
explicit R-symmetry breaking
In global SUSY
Intriligator,Seiberg and Shih showed in global SUSY
![Page 4: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/4.jpg)
SUSY breaking vacuum has a positive vacuum energy in global SUSY.
supergravity effect should be considered
to realize a Minkowski vacuum (V=0).
0|| 2WV global
)3(| ||| 22 WDWeV K
local
R-symmetry in supergravity
1. Are there relations between R-breaking and SUSY breaking like the Nelson and Seiberg’s argument?
R-symmetry should be broken for Majorana gaoujino masses to exist.
R-symmetry should be broken explicitly to avoid R-axion and …. 2. In O’Raifeartaigh Model ,which generally has SUSY
breaking vacua,are SUSY breaking vacua metastable ?
![Page 5: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/5.jpg)
Contents of our study and this talk
1. the relation between R-symmetry and Supersymmetry breaking in supergravity(SUGRA)
(based on the study of Nelson and Seiberg)2. the metastability of a supersymmetry breaking
Mikowski vacuum in O’Raifeartaigh Model in SUGRA. (Intriligator ,Seiberg and Shih argued this
metastability in global SUSY.)3. Conclusion
We discuss,
![Page 6: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/6.jpg)
“The Nelson and Seiberg argument in global SUSY”
the generic R-symmetric superpotential is rewritten
;R[W]=2,R[X]=qX.If there are R-breaking SUSY vacua( ),
There is not a solution of these equations. R-symmetry breaking SUSY breaking
1.The relation between R-symmetry and SUSY breaking in SUGRA
N+1 equations with N unknowns
(i=1,2,…,N)
![Page 7: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/7.jpg)
In SUGRA ,F-flat conditions are modified
That is ,as long as , Nelson and Seiberg’s argument still holds.For example, in the model with and , R-symmetry breaking SUSY
breaking. But most of R-symmetric Models don’t cause R-
breaking. We considered O’Raifeartaigh Model which is known as the R-symmetric Model drawing SUSY breaking.
![Page 8: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/8.jpg)
3.The metastability of SUSY breaking vacua
We argue explicit R-symmetry breaking makes SUSY breaking vacua metastable in O’Raifeartaigh Model.
Before the main topic,
: a=1,2,…,r and i=1,2,…,s. And r>s . In global SUSY, F-flat conditions for X are
so that there is no supersymmetric vacuum.
Introduction of generic O’Raifeartaigh Model
r equations with s(<r) unknowns
![Page 9: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/9.jpg)
Intriligator ,Seiberg and Shih’s argument
They added explicit R breaking terms to the generic O’Raifeartaigh Model to avoid R-axion.
In global SUSY, F-flat conditions for X areThere are solutions
depending on f.
SUSY breaking vacuum is metastable!
Explicit R-breaking
V
X
R-symmetric
SUSYSUSY
![Page 10: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/10.jpg)
and add
SUSY breaking vacuum:
SUSY vacuum:
The SUSY breaking vacuum is metastable and long-lived for .
Example in global SUSYV
XSUSYSUSY
)/1( O
![Page 11: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/11.jpg)
The metastability in SUGRA Generic O’Raifeartaigh Model in SUGRA
F-term flat conditions for X are
If there is no solution of ,
there is no SUSY vacuum .For example, K is canonical.
This potential can be
negative
r equations with s(<r) unknowns
![Page 12: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/12.jpg)
And if Kahler is canonical, V>0 .
Explicit R-breaking terms are required not only to avoid R-axion but also to make a Minkowski vacuum
under this condition about K.
This adding makes SUSY breaking vacuum metastable!
This adding makes the solutions of these equations exist.
The points satisfying the F-flat conditions are in V<0.
..
![Page 13: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/13.jpg)
By adding more generic explicit R-breaking terms,
Even if SUSY vacuua actually exist.
But this constant |c| must be set to tune V to 0.
There is a possibility the SUSY breaking Minkowski vacuum is not metastable .
SUSY vacua appear like the analyses in global SUSY.
If c is small, this is the same as in global SUSY!
![Page 14: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/14.jpg)
case 1 : By integrating out and , SUSY breaking vacuum(V=0): SUSY vacuum:case 2 : SUSY breaking vacuum (V=0) :
SUSY vacuum : ( )
In these cases, SUSY vacuum cannot exist!
Example(1)
![Page 15: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/15.jpg)
The situations to avoid the metastable
More generally ,the solutions of F-flat conditions can be expressed.In this case , the condition for SUSY vacua to exist is
In Polonyi –like Model,
SUSY breaking vacuum(V=0):
,this condition is
SUSY vacua can’t exist.
![Page 16: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/16.jpg)
(2)
The parameters are set ; SUSY breaking vacuum(V=0)
SUSY vacuum
V
XSUSY
SUSY
)/1( O
This term is added to (1).
Example 2
![Page 17: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/17.jpg)
SUSY vacua appear , . 0 makes the SUSY breaking vacuum
long-lived .
Even if = 0 , It is possibile that a SUSY vacuum exist . But the constant |c| is fixed to tune V to 0 ,so that there is a possibility that a SUSY Minkowski vacuum is
stabilized.
That is,…… cXfW ),( R
We found Polonyi-like models can avoid the metastable.
![Page 18: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/18.jpg)
4.ConclusionNelson and Seiberg argument “In the model with global U(1)R symmetry,R-symmetry breaking SUSY
breaking “This argument is also satisfied in SUGRA under the special condition , .(R[X]= )For example , The R-charges of all fields are positive , and .
![Page 19: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/19.jpg)
We considered R-symmetric Model with SUSY
breaking dynamics, O’Raifeartaigh Model.To make gauginos massive and avoid R-axion,R-symmetry should be broken explicitly.In global SUSY ,Intriligator Seiberg and Shih
showed the requirements cause the metastability of SUSY breaking vacua.
We discussed the metastability in supergravity.
![Page 20: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/20.jpg)
If Kahler potential is canonical, V >0 in O’Raifeartaigh Model in
supergravity. Explicit R-symmetry breaking terms are required not only to avoid R-axion but also make Minkowski vacua.
The explicit R-symmetry breaking causes the metastable Minkowski vacuum under the condition .We verified there are the points which satisfy SUSY stational conditions in the explicit R-symmetry breaking models.It is possible that the metastability of the SUSY breaking Minkowski vacuum is avoided ,for example, in Polonyi-like Model. Fin
.
.
![Page 21: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/21.jpg)
Appendix
There is a R solution satisfying SUSY stational conditions in the case R-charge of X is negative.
A solution which doesn’t satisfy the NS condition.
SUSY :
SUSY :
X
V
SUSY
qx<0
![Page 22: Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity](https://reader035.vdocuments.us/reader035/viewer/2022062305/56816267550346895dd2d352/html5/thumbnails/22.jpg)