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Dynamical SUSY Breaking in
Meta-Stable Vacua
Ken Intriligator, UCSD
DPF 2006, 10/31/2006
KI, Nathan Seiberg, and David Shih
hep-th/0602239
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Dynamical Supersymmetry Breaking:
• No explicit breaking:
• Vacuum spontaneously breaks SUSY.
• SUSY breaking related to some dynamical
scale
Can naturally get hierarchies (Witten).
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Dynamical SUSY breaking is hard
• Witten index: All SUSY gauge theories with
massive, vector-like matter have
SUSY vacua. So DSB seems to require a chiral
gauge theory. (Some exceptions, with massless,
vector-like matter.) DSB looks non-generic.
• Most of our techniques to analyze SUSY theories
are based on holomorphy/chirality/BPS.
SUSY breaking depends on the Kahler potential
which is hard to control.
Perhaps we should try a new approach...
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Perhaps we're in a long-lived false vacuum
V
You are here. (?)
maybe unbroken
SUSY elsewhere
fields
Old idea, with renewed prominence in string theory
and cosmology. Accepting the possibility, we find
much simpler models of DSB. E.g. good, old SQCD!
Suggests meta-stable DSB is generic.
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Review of N=1 SQCD
When all the quarks are massive,
there are
SUSY vacua.
V
For
with
and
the susy vacua
are at
where coupling
is strong. Analyze near origin
in dual variables (i.e. in the
low energy effective field theory)...
?
M
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The IR dual theory (Seiberg '94)
Electric
Focus on
where
the Seiberg dual theory is IR free.
Magnetic
UV cutoff of this IR free theory is
.
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Rank condition SUSY breaking.
Key point: the Kahler potential for the IR free fields
is smooth near the origin, so there it's of the form:
SUSY broken at tree level!
(rank Nf -Nc )
(rank Nf )
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Dual theory yields the potential
V
wait...
expected
susy vacua,
via non-pert
effects
Susy broken at tree level at origin.:
M
Up to here was known 12 years ago.
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DSB vacua near the origin, via dual
Classical vacua (up to global symmetries) with broken SUSY:
Pseudo-moduli:
Arbitrary
and
matrices
DSB:
Pseudo-flat directions are lifted in the quantum theory
(typical of tree-level breaking).
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Pseudo-moduli get a potential at 1-loop
in the magnetic theory
Use
1-loop effective potential for pseudo-moduli:
mass matrices are
functions of the
pseudo-moduli
1-loop vacuum energy
Higher loops (higher powers of small
) are
smaller, because the magnetic theory is IR free.
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Effect of the one-loop potential for the
pseudo-moduli
The effective potential is minimized (up to symmetries):
All pseudo-moduli get non-tachyonic masses at one-loop.
SUSY broken:
Vacua (meta) stable (we'll discuss tunneling soon).
Vacua mysterious in electric description.
Not semi-classical, very quantum mechanical.
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Effects from the microscopic theory
There are (uncalculable) contributions to
from
high energy modes (
), e.g. loops of SUSY split
massive particles. Is this a problem?
No.
All such effects can be summarized by corrections to the
Kahler potential and lead to effects which are real analytic
in
. Our calculated
is not real analytic
in
, because it arises from integrating out modes
which are massless as
.
Corrections from UV modes are thus negligible for
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Dynamical SUSY restoration
SUSY vacua, in magnetic theory via:
Non-perturbatively restores SUSY in the magnetic theory.
In free magnetic range,
, this term is
insignificant for the DSB vacua near the origin.
, so
For
, can reliably analyze effect
of this term elsewhere, and find the SUSY vacua in the
magnetic theory, staying below its cutoff:
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Sketch of the full potential
V
cutoff
Effect of
(meta-)stable DSB
Nc SUSY vacua
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Lifetime of meta-stable DSB vacua
Estimate height and width of potential:
Barrier not high, but
it's extremely wide.
.
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Lifetime of DSB vacua, cont.
Decay probability
(e.g. Langer,Coleman)
Estimate classical, Euclidean action of bounce:
Our meta-stable DSB vacuum is parametrically
long-lived for
.
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Compact moduli space of DSB vacua
(SSB)
DSB vacua:
Large configuration space of vacua. Massless goldstone
bosons and goldstino.
vs
Electric description: naively no massless fields, since quarks
have masses and SYM has a mass gap. (True in susy vacua.)
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Prospects for Model Building
Longstanding model building challenges:
• Naturalness.
• Direct gauge mediation leads to Landau poles.
• R-symmetry problem.
They can be revisited.
The new DSB mechanisms offer new perspectives
on these issues and provide new avenues for
model building.
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E.g. the R-symmetry problem
DSB without SUSY vacua: non-generic superpotential or a
U(1)R symmetry. (Affleck, Dine, Seiberg; Nelson, Seiberg).
For nonzero Majorana gluino masses, U(1)R should be broken.
To avoid a Goldstone boson, U(1)R should be explicitly broken,
which might restore SUSY. (Gravity may help.)
Our examples: no exact U(1)R. (Indeed, SUSY vacua.)
Meta-stable DSB vacua have accidental approximate U(1)R.
Perhaps it is better if that symmetry is also spontaneously
broken.
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Comments on Cosmology
V
Very gentle slope. Useful for inflation
or quintessence?
. .
. .
. .
susy
Quic kT i me™ and a
T IFF (Unc ompres s ed) dec ompres s or
are needed t o s ee thi s pi c ture.
Larger configuration space of DSB vacua. Can
favor populating DSB vacua. Also,thermal Veff
favors populating the DSB vacua.
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Outlook
• Accepting meta-stability leads to surprisingly
simple models of DSB.
• new avenues for model building.
• Suggests meta-stable DSB is generic in N = 1
SUSY field theory, and in the landscape of string
vacua.
• Extend to the landscape of string vacua. Relate to
anti-D-branes in KS geometry? (note: baryonic).
Counting vacua.
• Cosmology.
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