SUPERSYMMETRY BREAKING AND THE RADION IN ADS BRANE WORLDS

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1 SUPERSYMMETRY BREAKING AND THE RADION IN ADS BRANE WORLDS YAEL SHADMI, TECHNION Andrey Katz, Michele Redi, YS, Yuri Shirman, th/ Andrey Katz, YS, Yuri Shirman, th/

2 essential ingredient of brane world models (flat/warped): R determining R -- radion stabilization detuned RS R fixed (brane tensions detuned):

3 but 4d: AdS/dS classically can radiative corrections (due to gravity, other bulk fields) take us back towards Mink_4?

4 supersymmetric detuned RS: can break SUSY by b.c. (not in RS) radiative corrections finite and calculable

5 simple example of moduli stabilization in AdS backgrounds: one scalar (r) stabilized classically second scalar stabilized at 1-loop

6 supersymmetric detuned theory: AdS5 with curvature k exp(-k r) Bagger Belyaev Redi Lalak Matyszkiewicz T0 T 1 ( TT0 )( TT ) ln 3 R T 6M5k 2 k ( TT )( TT ) 0 T SUSY: need: 1) 0, T

7 4d: AdS_4 curvature radius L 1 4k L 2 2 T T T T 0 0 detuning 2) brane mass terms for gravitino: kL 0 exp kr ( ) susy spontaneously broken if 0 exp( kr ) exp( i ) exp( kr) 0 nonzero phase: SUSY broken ( NOT IN RS! ) downstairs : breaking by bc

8 susy breaking and graviphoton : 5d SUGRA multiplet: graviphoton BM U(1)_R gauge field gravitino charged under U(1)_R : phase of can be compensated by graviphoton Wilson line b B 5 dx 5 0 so: b parametrizes SUSY breaking: SB for b 0

9 to summarize: supersymmetric model, detuned brane tensions susy broken for nonzero b will always take 1 T T k L T T0 1 small detuning perturb around RS

10 4d radion effective theory: Bagger Redi T r ib W M L 2 4 (1 e kr e 3kT ) k ( TT ) 2 1 e 1 4 2kR 2 K 3M ln + O( ) 1 e L RS V V ( r) no b dependence: b mod ulus note similarity to KKLT --- but perturbative Luty Sundrum

11 but: DTW 1 exp( 3 ikb) susy unbroken only for zero b no scale: V indep of b, susy broken everywhere here: V indep of b, susy broken for nonzero b

12 quantum corrections susy breaking: loop corrections to cc breaking non-local: loop cutoff by compactification scale: finite calculate using: KK spectrum 4d radion theory many simplifications possible

13 KK spectrum gravitini: (only calculated this because it s the only thing we need) RS detuning: splittings 1/L + 1/L^2 susy breaking

14 KK V = V(fermions) + V(bosons) = V(fermions) V (fermion s) SUSY for small susy breaking 1 1 L 1 2 L to leading order in detuning 1/L: can use flat space propagators can only solve analytically for k R 1

15 4d radion theory W M L 2 4 V kr 3kT (1 e e ) 1 L 2 1 L to leading order in 1/L, can take zeroth order in Kahler = zeroth order in detuning RS Kahler potential V from W + K RS 1-loop 1-loop Gregoire Rattazzi Scrucca Strumia Trincherini Falkowski

16 loop: Kloop = Kloop(T+Tbar) Vloop ~ sin^2 (3kb/2) Vloop maximal SUSY breaking unbroken susy b stable --- AdS 2 stable extrema: b=0 unbroken SUSY b=pi/(3k) maximal breaking b stabilized radiatively

17 sign of loop contribution: <0 pure gravity >0 hypers so with a few hypers can get positive contribution and potentially cancel tree-level cc size of loop contribution: loop factor non-local (susy breaking) e kr

18 can loop correction be significant? YES roughly: imagine lowering 5d curvature k: Vtree becomes shallow [no classical potential in flat case] Vloop does not [even in flat case have nonzero Casimir energy]

19 consider c=1/2 hypers: (simplest: give -1/2 gravity contribution) V V loop tree N H 1 1 (loop factor) 2 ( kr) 2 kr<<1: can overcome loop suppression note loop expansion still fine for small NH

20 1/L << k << 1/R with hypers: Vloop ~ + sin^2 (3kb/2) loop correction can (almost) cancel tree SUSY: global minimum (at b=0) loop expansion reliable maximal SUSY breaking: saddle point: maximum along b, minimum along r V b stable as long as 4d cc<0 b mass above BF bound

21 in principle, can make 4d cc arbitrarily small in practice: only need cc 4 (TeV)

22 outlook: model building: imagine embedding MSSM: soft mass at most 1/L so far: a very simple potential (only gravity + c=1/2 hypers): one relevant free parameter (kr) cannot get cc < (soft mass)^4 but may be possible in more complicated model

23 to conclude: supersymmetric detuned RS: radius stabilized susy broken negative 4d cc can be offset by Casimir energy (here very minimal model) classical modulus stabilized by loop correction in AdS novel mechanism of stabilizing radion in almost flat extra dimensions (k<<1/r)