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MAGNETIC
SUPERSYMMETRY
BREAKING
Based on :
W. Buchmuller, M.Dierigl,E.D & J. Schweizer,
arXiv:1611.03798 [hep-th]
jan. 17, 2017
III Saha Theory Workshop
Kolkata
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Outline
1) Higher-dimensional completions of the
Standard Model
2) Magnetic compactifications
3) Effective field theory
4) Quantum corrections, Wilson lines as
goldstone bosons
5) Conclusions
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1) Higher-dimensional completions
of the Standard Model
 Structure of Standard Model points towards Grand
Unification (matter content, gauge group, unification
of gauge couplings,neutrino masses)
 Strong theoretical arguments for supersymmetry at
high scales (gravity,string theory)
 Extra dimensions unavoidable in string theory
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Extra dims. do address:
-
Unification of all forces (including at TeV energies)
Holographic solutions to the hierarchy problem (RS)
New ways to break SUSY: Scherk-Schwarz
New models of inflation
- Sometimes higher-dim. symmetries protect quantum
corrections in a way invisible from 4d.
Ex: Internal comp. of a gauge field protected by
gauge symmetry
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Orbifolds are a natural framework to compactify
higher-dimensional theories:
- Fermion chirality
- Doublet-triplet splitting in orbifold GUT’s
- Partial or total supersymmetry breaking
• Compactification scale
defines the GUT/unification scale.
• Scale of supersymmetry breaking
usually much smaller.
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usually
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2) Magnetic compactifications
Widely studied in string theory (« intersecting
branes »), few papers in field theory.
Consider a 6-dim. theory :
An internal magnetic field
- break SUSY, due to the magnetic moment coupling
- Turns KK states
where
into Landau levels
is the internal helicity of particles.
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, mass
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• An internal magnetic field is quantized
,
N = integer flux
• Each Landau level is N times degenerate.
• Precisely N chiral fermion zero modes.
• Starting with a SUSY 6d theory, it is usually said that
the effect of the magnetic field is to add a D-term
Fayet-Iliopoulos (FI) term in 4d
 Potential relevance to inflation
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Split symmetries
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One example (Buchmuller, Dierigl,Ruehle,Schweizer, 2015,2016) :
WB, Dierigl, Ruehle, Schw
nsider
SO(10)
GUT
group
6d,broken
brokenatatorbifold
orbifold
fixed po
- SO(10)
GUT
model
inin
6d,
fixed
ndardpoints,
SU(5)xU(1),
Pati-Salam
SU(4)xSU(2)xSU(2)
and flippe
Standard
Model in
4d
(5)xU(1), with Standard Model group as intersection; bulk fi
16*,
10’sfields
[Asaka, WB, Covi ’02,’03]; full 6d gauge symmetry:
- Bulk
SO(10) ⇥ U(1)A
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In 4d there are N 16’s from charged bulk 16-plet
N flux
quanta
: 16-plet and N flux quanta:
Nwith
16’s from
charged
bulk
c
16 [SO(10)] ⇠ 5⇤ + 10 + 1 [SU(5)] ⇠ q, l, uc , ec , dc , ⌫
[GSM ]
- Higgs fields from uncharged bulk 10-plets form split
multiplets.
- Magnetic flux break SUSY (Bachas;95); « soft » SUSY
breaking only for quark-lepton families:
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However, not enough; there is no mass gap:
soft massed given by the FI term of the same order (
) as the masses of Landau levels
one needs an effective theory for the whole tower.
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3) Effective field theory
• Consider an abelian 6d SUSY theory compactified on
a torus.
N=2 SUSY in 4d before the magnetic flux;
4d Multiplets:
vector
charged hyper
6d effective action in superfields: (Marcus,Sagnotti,Siegel ;
Arkani-Hamed,Gregoire,Wacker)
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are internal components of gauge fields =
Wilson lines
Mode expansions with flux:
where (harmonic oscillator
algebra)
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The final 4d effective action for Landau levels is
FI term
Mass terms
One also found the effective action for the non-abelian
case
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4) Quantum corrections, Wilson lines as
goldstone bosons
Interested in Higgs = internal component of the gauge
field. 6d gauge symmetry could protect its mass ?
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Each contribution is quadratically divergent: the sum
of the whole tower is however exactly zero !
◆
X Z d4k ✓
n
n+ 1
2
2 2
δmb = −4q g |N|
− 2
1
3
4
2
(2
⇡
)
k
+
↵
(n
+
)
k
+
↵
(n
+
2
2)
n
✓
◆
Z1
2 2
X
1
3
qg
1
= − 2 |N|
dt 2 ne− ↵ (n+ 2 )t − (n + 1)e− ↵ (n+ 2 )t
4⇡
t
0
n
0
1
1
1
Z1
2 2
qg
1 @ e2 ↵ t
e2 ↵ t A
= − 2 |N|
dt 2
− ↵t
= 0
↵
t
2
2
4⇡
t
(e − 1)
(e − 1)
0
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'
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sonic cont ribut ions t o t he Wilson line mass wit h
The same is true for the fermionic contribution
χ n ,j
'
'
χ̃ n ,j
mionic
cont a
ribut
ion t o
t he Wilson
line mass wit
Is there’s
symmetry
reason
?
mionic fields,
X
qg
n ,j
p
⇣
⌘
↵ (n + 1)
'
Q̃ n + 1,j Q̃ n ,j − Q n ,j Q n + 1,j
+
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Action of charged matter fields invariant under
translations
Symmetries for constant Wilson line background
Flux background breaks the symmetries spontaneously
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Translational symmetries now non-linearly realized
with Wilson lines as Goldstone bosons
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Conclusions, Perspectives
 Strong theoretical arguments for SUSY at high
scales: gravity, string theory
 Energy scale of grand unification
GeV
Scale of SUSY breaking
?
 Magnetized compactifications : high-scale SUSY
breaking
 Hope for a higher-dim. protection of scalar masses:
Higgs mass, inflaton.
 Various applications possible: moduli stabilization,
inflation, orbifold GUT’s.
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Thank you
E. Dudas – E. Polytechnique