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Moduli stabilization and flavor structure in 5D SUGRA with multi moduli Yutaka Sakamura (RIKEN) in collaboration with Hiroyuki Abe (Yukawa Inst.) June 17,

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Introduction Problems in Standard Model gauge hierarchy problem Yukawa hierarchy Charge quantization Anomaly cancellation GUT? SUSY? … flavor sym., extra dim., …

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0 RR y f (0) i Yukawa hierarchy from extra dimension e.g.) zero-mode: 5D mass (Arkani-Hamed & Schmaltz, PRD61(2000)033005;…) (4D Yukawa) = (overlap integral)

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In 5D SUGRA, : Radion (chiral) multiplet Flavor-dependent SUSY breaking (e.g. Scherk-Schwarz SUSY breaking) Yukawa hierarchy SUSY flavor problem

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5D SUGRA with Multi moduli Yukawa hierarchy SUSY breaking cf.) In string context, “Mirror mediation”, Conlon, JHEP0803 (2008) 025

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5D (off-shell) SUGRA on S /Z Field content Weyl multiplet: Vector multiplet: (One of them is the graviphoton multiplet.) Hypermultiplet: 1 2 compensator physical (Kugo & Ohashi, ) where Norm function

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5D Lagrangian bulk part (bulk mass) (gauge coupling) =

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T = zero-mode of Single modulus case: I I T is the radion multiplet. Radius: Moduli:

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5D SUGRA with multi moduli Field content Vector multiplet: Hypermultiplet: Orbifold parity Yukawa hierarchy SUSY gauging matter

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4D effective theory Soft SUSY parameters physical Yukawa coupling (cf. H.Abe & Y.S., PRD75 (2007) )

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Single modulus case tachyonic soft masses from F X (cf. H.Abe’s talk)

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Multi moduli case If the second term of dominates and, No SUSY flavor problem

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e.g.) All moduli are stabilized. Vacuum

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In this case, When the second term dominates. Positive soft squared masses No SUSY flavor problem from KK vector multiplets

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Integration out for 5D gauge coupling

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When, RR y Integration out for

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When, RR y Integration out for

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Physical vector multiplets Vecter multiplets (I=1,2,…,n) : parity-odd : parity-even Superconformal gauge-fixing … (# of physical vector multiplets) = n-1 Single modulus case: no KK vector multiplets

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RR 0y Single modulus case: sequestered Multi moduli case: not sequestered When

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Summary 5D SUGRA with multi moduli Yukawa hierarchy SUSY breaking Radius: Additional contribution to the Kahler potential can save Tachyonic sfermion masses at tree level SUSY flavor problem

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