Realization of spontaneous
gauge and supersymmetry breaking vacuum

Yuji Omura (KMI, Nagoya Univ.)

based on 1705.00809
collaboration with T. Kobayashi, O. Seto, K. Ueda

Outline• Introduction• SUSY breaking associated with gauge symmetry
breaking.
gauge U(1) modelPati-Salam• SummaryIntroduction• I would like to talk about SUSY breaking in models
with gauge symmetries.

Introduction• I would like to talk about SUSY breaking in models
with gauge symmetries.

• One motivation is“unify GUT breaking and SUSY breaking sectors”

SM gaugeinteraction

MSSM

GUT
sectormessenger
sector
Yukawacoupling

SUSY
sectorIntroduction• I would like to talk about SUSY breaking in models
with gauge symmetries.

• One motivation is“unify GUT breaking and SUSY breaking sectors”

SM gauge
interaction

MSSM

GUT
sectormessenger
sector
Yukawacoupling

SUSY
sector• Another motivation is
to solve the problems concerned with SUSY breaking.
Problems about SUSY breaking

• Another motivation is
to solve the problems concerned with SUSY breaking.
Problems about SUSY breaking
SUSY model consists of superpotential (W: holomorphic func.) and Kahller.
W contributes to the scalar potential as
V(W(I) =II)I

2+(VD (I ))• Another motivation is
to solve the problems concerned with SUSY breaking.
Problems about SUSY breaking
SUSY model consists of superpotential (W: holomorphic func.) and Kahller.
W contributes to the scalar potential as
V(W(I) =I

If SUSY is conserved,II)
I

2+(VD (W = 0 (V = 0) :I ))• Another motivation isto solve the problems concerned with SUSY breaking.
Problems about SUSY breaking
SUSY model consists of superpotential (W: holomorphic func.) and Kahller.
W contributes to the scalar potential as
V(W(I) =II)I

2+(VD (I ))In typical SUSY breaking models,W = fXW=f =0
X

V = f2
X is ﬂat• Another motivation isto solve the problems concerned with SUSY breaking.
Problems about SUSY breaking
SUSY model consists of superpotential (W: holomorphic func.) and Kahller.
W contributes to the scalar potential as
V(W(I) =II)I2+(VD (I ))In typical SUSY breaking models,W = fXW=f =0
X

Phase rotation of X is namely R-symmetry,
and it is crucial to SUSY breaking.

V = f2
X is ﬂat

Problem 1

Spontaneous SUSY breaking seems to imply the existence of R-symmetry inthe models.
Rcharge [W ] = 2(Nelson,Seiberg,hep-th/9309299)

R-symmetry forbids gaugino masses.

Problem 1

Spontaneous SUSY breaking seems to imply the existence of R-symmetry inthe models.
Rcharge [W ] = 2(Nelson,Seiberg,hep-th/9309299)

R-symmetry forbids gaugino masses.
Our vacuum have to break both R-symmetry and SUSY:

Problem 1

Spontaneous SUSY breaking seems to imply the existence of R-symmetry inthe models.
Rcharge [W ] = 2(Nelson,Seiberg,hep-th/9309299)

R-symmetry forbids gaugino masses.
Our vacuum have to break both R-symmetry and SUSY:
W = f X + Xw( )and SUSY is broken,
but scalar comp. of X is flat@tree
XW = 0hXi 6= 0<latexit sha1_base64="DP7fSQ2/nZDc3+Oze4vZAoJmVDo=">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</latexit>

for R-symmetry breaking

Problem 1

Spontaneous SUSY breaking seems to imply the existence of R-symmetry inthe models.
Rcharge [W ] = 2(Nelson,Seiberg,hep-th/9309299)

R-symmetry forbids gaugino masses.
Our vacuum have to break both R-symmetry and SUSY:
W = f X + Xw( )Problem 2and SUSY is broken,
but scalar comp. of X is flat@tree
XW = 0hXi 6= 0

for R-symmetry breaking<latexit sha1_base64="DP7fSQ2/nZDc3+Oze4vZAoJmVDo=">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</latexit>

The scalar comp. of X may be stabilized by the radiative correction,
but not so simple. (Often stabilized at X=0.)(Shih,hep-th/0703196;Sun,0810.0477)

Problem 3

Even if R-symmetry is broken, obtaining gaugino mass is not trivial.
(Komargodski,Shih,0902.0030)

Problem 3

Even if R-symmetry is broken, obtaining gaugino mass is not trivial.
One illustrative R-symmetric model

W = fX + X +X = vX +2

F+ m1 X+

(Komargodski,Shih,0902.0030)+ m2 X+Messengers charged under SM gauge symmetry

Problem 3

Even if R-symmetry is broken, obtaining gaugino mass is not trivial.
(Komargodski,Shih,0902.0030)

One illustrative R-symmetric model

W = fX + X +X = vX +2

F+ m1 X++ m2 X+

Messengers charged under SM gauge symmetry

Even if φ+/- and X+/- are integrated out at the origin,d2b (ln m1 m2 ) W W

gaugino mass is vanishingProblem 3

Even if R-symmetry is broken, obtaining gaugino mass is not trivial.
(Komargodski,Shih,0902.0030)

One illustrative R-symmetric model

W = fX + X +X = vX +2F+ m1 X++ m2 X+

Messengers charged under SM gauge symmetry

Even if φ+/- and X+/- are integrated out at the origin,d2b (ln m1 m2 ) W W

gaugino mass is vanishing

Motivated by those problems, I propose a model where φ+, φ-, X+,
X- are charged under extra gauge symmetry.
Then, we ﬁnd a realistic vacuum to cause SUSY breaking inassociation with gauge symmetry (GUT) breaking.

SUSY breakingassociated with gauge symmetry breaking

For the demonstration, let me consider the U(1) case:(Kobayashi, Seto,YO,Ueda,1705.00809)
Matter contents

Chiral superfield±X±X

SMsingletsingletsinglet

U (1)
±1±1
0

U (1)R02
2

superpotential

W = fX + X ++ m1 X++ m2 X+U(1) D-termg2
VD =| + |22|2| + |X+ |

2|X |

2 2

Important point is that there is no vacuum where all F-terms arevanishing in this model.

For the demonstration, let me consider the U(1) case:(Kobayashi, Seto,YO,Ueda,1705.00809)
Matter contents

Chiral superfield±X±X

SMsingletsingletsinglet

U (1)
±1±10

U (1)R022

superpotential

W = fX + X ++ m1 X++ m2 X

U(1) D-term
2g
VD =| + |22|

2| + |X+ |2|X |2 2+XW = f +X+W = m2 +X+ W = m1

Important point is that there is no vacuum where all F-terms arevanishing in this model.

sketch of the scalar potential
NoteThis runaway vacuum is proposedby Azeyanagi, Kobayashi, Ogasawara,Yoshioka,1106.2956;1208.0796! = !# + !%! = !# + !%!% ./01234 10 5ℎ.7 89:03!%!# .7 ;.0.;<; 10 5ℎ.7 9.03

0+(/*!#2<0:=:> ?:@<<;

R-symmetry breaking&, &(/*sketch of the scalar potential
Kobayashi,YO, Seto,Ueda,
1705.00809! = !# + !%! = !# + !%!% ./01234 10 5ℎ.7 89:03

our vacuum!%!# .7 ;.0.;<; 10 5ℎ.7 9.03

0+(/*!#stabilizedby one-loop

2<0:=:> ?:@<<;

R-symmetry breaking&, &(/*Important points of this vacuum
・There is a runaway direction and stabilized by one-loopcorrection. Then, R-symmetry is also spontaneously broken.

Important points of this vacuum
・There is a runaway direction and stabilized by one-loopcorrection. Then, R-symmetry is also spontaneously broken.
・The runaway behavior is one generic feature of this kind ofmodel, where VF is non-vanishing anywhere.

When

I

= vI satisfies

J =0V
=WW
FIJI

there is flat direction (z) in VF:

2gAVD =2† A
I qIJ2L

I = vI + WI (v) z

ˆ I = vI + WI (v)z + cIz2gA
VD |WIJ WJ =0 =21A
vI qIJ cJ + c.c. + O(z 2 )zbecause of the gauge symmetry(Azeyanagi, Kobayashi, Ogasawara,Yoshioka,1106.2956;1208.0796)

・We have discussed a simple U(1) model:
U(1) → nothing

・We have discussed a simple U(1) model:
U(1) → nothing
・We can extend this to GUT symmetry:
If the ﬁelds, φ+/- and X+/-, are charged under GUT symmetry(e.g., Pati-Salam, ﬂipped SU(5) etc.),
SU(2)R ×SU(2)L ×SU(4) → SM
SU(5) ×U(1) → SM
GUT breaking and SUSY breaking are unified.

Let’s consider the application to “Pati-Salam” (SU(4)×SU(2)R×SU(2)L).
(Kobayashi,YO, Seto,Ueda,1705.00809)

The charge assignment of φ+/- and X+/-

Superpotential

W = f X + XT r( +) + m1 T r(X+) + m2 T r(X+)

Let’s consider the application to “Pati-Salam” (SU(4)×SU(2)R×SU(2)L).
(Kobayashi,YO, Seto,Ueda,1705.00809)

The charge assignment of φ+/- and X+/-Superpotential

W = f X + XT r( +) + m1 T r(X+) + m2 T r(X+)

We can find the runaway direction that breaks R-symmetry,
and we obtain the SUSY breaking vacuum at the one-loop.
Fm1,2±=

0000000

X± =±z00000000

SU(2)R ×SU(4) → SU(3)×U(1)YFX± =±F0000000

• Another interesting point of this setup isgaugino mass is generated by the gauge messenger
contributions.
Massive gauge bosonsfrom SU(2)R SU(4) breaking

λiλiThe fermionic partners
gauge messenger contribution

4Fbaz0b2 ,b3 ) = ( 10/3, 0,Ma =where( bYa1)

Summary
・How to break SUSY spontaneously is one of the crucial
issues.

・SUSY breaking model generally has R-symmetry.
→ Both R-symmetry and SUSY should break down at our vacuum.

・I introduce one type of SUSY breaking models:Gauge symmetry causes a runaway direction to break R-symmetry. Our vacuum isinduced by stabilizing the runaway according to the one-loop correction.
・I gave some comments on the applications to GUT models inour paper. The detail will be shown near future.
ENDBackup

Comments (Kobayashi,YO, Seto,Ueda,1705.00809)• Wino mass is vanishing at LO in the Pati-Salam. Other contributions
like gravity mediation may be required.

• This mechanism can be applied to other GUTs, e.g., flipped SU(5).
• One issue of this mechanism is about tachyonic masses of sfermions.
one-loop contribution: almost vanishing at our vacuum.
two-loop contribution: we need more careful study.

• Spontaneous R-symmetry breaking leads massless R-axion.
Gauged U(1)A instead of R-symmetry does work well.
N. Maekawa,Y. Shigekami, M.Yoshida,1712.05107

Gauged U(1)A Model(Maekawa,YO,Shigekami,Yoshida,1712.05107)

Matter contents

Chiral superfield
SSM
singletsingletU (1)As
1
1

Superpotentials

W = a0 + a1 S

Wef fa2+2

a0 + (a1 s )Ss

S

2

2a3+6sS

is obtained when λ<<1.

U(1)A D-term potentialg2
VD =22| | + s|S|2 23+ ...

Effective Potential for S in SUGRA
1 2 2 4Vef f = f + |W S ||S| + g sD0 |S| + g s |S|222222a20afa0
3 2 + (S + S † ) 2 + 02 |S|2 + . . .
Mp
Mp
Mp

(originated from constant term, a0, in W)! = !# + !%(Maekawa,YO,Shigekami,Yoshida,1712.05107)

SUSY is broken.
: ;<==>?@< A; B@CD>E B< FGH:I >JJ>K?
! = !# + !%0accidental “R-symmetry” breaking! = 0 )*+,-Θ&