flux compactification and susy...
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Flux Compactification and SUSY Phenomenology
Komaba07On occasion of Prof. Yoneya’s 60th birthday
Masahiro YamaguchiTohoku University
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Talk Plan
• Introduction : Flux compactification and KKLT set-up
• Naturalness Problem of Weak Scale• Warped Superstring Compactification• SUSY phenomenolog: mirage mediation
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String TheoryCandidates for1) Quantum Gravity (Yoneya)
2) Ultimate Unified Theory– gauge structure– matter representations– generations– Yukawa couplings – secret of weak scale
….I will discuss possible implications to TeV scale physics.
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Moduli Stabilization:A long-standing problem
• Moduli/Dilaton Stabilization– Moduli have not been stabilized at tree level.– Non-perturbative effects important
• Why moduli?– structure of compact dimensions– gauge & matter structure
• if light moduli– SUSY breaking– Cosmological implications
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Gaugino condenstate: runnaway potential
exponetial superpotentialrunaway scalar potential
How to avoid runaway?race track : multiple gaugino condensatesnon-perturbative corrections to Kaehler potential………
V
Re S
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Flux Compactificatons
• Switch on Fluxes: H(3) and F(3) type IIB side
• Consistent solution • Complex moduli & dilaton are stabilized
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• IIB superstring– 2-form potential (NS-NS, RR)– 3-form field strength
• superpotential for IIB theory
• complex moduli
• quantization of fluxes
(3,0) form
Gukov-Vafa-Witten ’99
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superpotential for complex moduli (z) and dilaton (τ)
• Consistent solution for flux compactifications in IIB– fluxes warped throat (Klebanov-Strassler throat)– W stabilizes complex moduli as well as dilaton– Kaehler moduli are not stabilized by fluxes
Giddings-Kachru-Polchinski 02
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KKLT set-up
• Potential for Kaehler moduli:non-perturbative effects
e.g. gaugino condensate on D7 brane
• case of single overall moduli:
• gauge kinetic function on D7:• superpotential from gaugino condensate
Kachru-Kallosh-Linde-Trivedi 03
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• Constant term in Superpotentialsimplest way to avoid runnaway behavior
• T modulus stablilized but with SUSY AdS vacuum
(Re T)
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• Up-lifting of the scalar potential– Adding SUSY breaking sector – Minkowski, SUSY broken vacuum
– KKLT: anti-D3 on top of warped throat– Dynamical SUSY breaking sector on D-branes can
also be OK
(Re T)
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Naturalness of Weak Scale
• Why is weak scale much smaller than Planck scale?• How is weak scale stabilized against radiative
corrections?
• Proposed Solutions:– Low energy supersymmetry– Large/Warped extra dimensions– Unknown strong dynamics
…..
• Ingredients in string theory. Question is which plays a crucial role.
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Warped Extra Dimension vs Low Energy SUSY in KKLT set-up
Similar set-up with different flux configurations and SM-brane configuration
Macroscopically (phenomenologically) important information: w_0, warp factor
warped extra dim. and low-E SUSY
large w_0strong warping
small w_0mild warping
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LHC (Large Hadron Collider) Experimentpp collider at CERNCenter of mass energy =14 TeVStarts 2007!Expects new physics discovery at TeV scale
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Warped Superstring Compactification at LHC
• Graviton Kaluza-Klein modes– Masses and Couplings different from those of
Randall-Sundrum model (Geometry of Klebanov-Strassler throat is very different from AdS5x X near top of warped throat)
• Resonances via Drell-Yan process Probe of (warped) extra dimension
Noguchi,Yamashita&MY 04
Drell-Yan cross section at LHCfor AdS5 x S1/Z2
Davoudiasl-Hewett-Rizzo ‘02
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Implications to Low-E SUSY• Original Motivation of KKLT:
realization of dS vacuum in string theory
• Simple KKLT set-up can also provide a new mediation mechanism of SUSY breaking.
• mixed modulus anomaly mediation = mirage mediation
Choi-Falkowski-Nilles-Olechowski-Pokorski 04,05Endo-MY-Yoshioka 05Choi-Jeong-Okumura 05
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Phenomenology with KKLT-like model
SUSY breaking sector added to uplift potential
Overall SUSY breaking characterized by gravitino mass:
SUSY breaking effect of Moduli T:suppressed by one-loop factor
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Gaugino Masses
@GUT scale
moduli+anomaly mediation: two contributions comparable
Consider SM on D7 brane
Gauge kinetic function
Gaugino Mass
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Gaugino Masses
For R~35 (KKLT),M1: M2: M3~1 : 1.3: 2cf.M1: M2: M3~1: 2: 7
(mSUGRA)
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Mirage Mediation
RG properties: Gauginomasses (as well as scalar masses) are unified at a mirage scale.
Choi, Jeong, Okumura 05
fromLebedev, Nilles,Ratz 05
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General Features of Mirage Mediation
• Compact Sparticle Mass Spectrum• small μ parameter (~M1)
small gluino mass/ RGE• LSP(lightest superparticle): neutralino
– admixture of gauginos and higginos• stau: tends to be light
• Mass Spectrum is very different from mSUGRA (CMSSM).gauge mediation & anomaly mediation
• Testable at future collider experiments (LHC/ILC)
Endo-MY-Yoshioka 05Choi-Jeong-Okumura 05
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Mass Spectrum: Case Study
n=1,l=1/3 n=3,l=0(KKLT)
Endo,MY,Yoshioka 05
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Conclusions
• Moduli Stabilization: Flux compactification• Implications to Weak Scale Stabilization• warped superstring compactification• low-E SUSY: mirage mediation
• LHC will provide crucial information beyond SM, and hopefully structure of unified theory.