1. Sebastián Franco Based on: F. Benini, A. Dymarsky, S. Franco, S. Kachru, D. Simic and H.Verlinde (to appear) KITP Santa Barbara SILAFAE January 2009 1

2. Motivation 2  Stabilization of Weak/Planck hierachySupersymmetry  Spontaneous SUSY breaking within MSSMSquarks ligher than u-quarks Gravity mediation Gauge mediation heavy (Planck scale) fields massive fields with SM charges Minimal Gauge Mediation  Gauge mediation solves the SUSY flavor problem (flavor blind)  Recently, interest in generalizations that include more general possibilities for messengers and their interaction with the hidden sector e. g. Meade, Seiberg and Shih Messengers: Messengers: (  charged under SM

3. 3  Today: new possibilities that are calculable via gauge/gravity duality Visible: SUSY extension of the SM. We assume visible, hidden and messenger matter in complete SU(5) representations. Hidden: strongly coupled SUSY field theory with metastable SUSY breaking at  S > 1 TeV. It has a global symmetry G  SU(5). They interact via:  In this General Gauge Mediation formalism, soft masses are parametrized by J h 2-point functions Meade, Seiberg and Shih  Geometrization: if the hidden gauge group has sufficiently large rank and gauge coupling, we may approximate the dual theory as a classical supergravity theory.

4. 4  Starting point:gravity dual with a SUSY breaking state at an exponentially small scale The model Deformed conifold with fluxes  Dual to the following gauge theory:  The D5-branes break conformal invariance and the theory undergoes a cascade of Seiberg dualities, which gradually reduces N and terminates in confinement.  Constructed from N D3-branes and M wrapped D5-branes at the conifold

5. 5  If N = k M – p (p << M), we are left with (M-p) probe D3-branes at the S 3 at the tip of the deformed conifold  The theory admits a metastable state with p anti D3-branes Kachru, Pearson and Verlinde  Each step in the duality cascade reduces N by M units  Confinement is dual to a deformation of the conifold. At the bottom (IR) of the throat there is a finite 3-sphere of size:

6. 6  Normalizable perturbationspontaneous SUSY breaking  There is a supergravity dual for this non-SUSY states (DKM): DeWolfe, Kachru and Mulligan vacuum energy

7. 7 global symmetry in 4dgauge symmetry in the bulk  The next step is to endow the hidden sector with a global symmetry. The SM gauge symmetry is a gauged subgroup of it Adding the ‘‘SM”: gauge symmetry in the bulk  In type IIB, this is achieved with a stack of D7-branes extending radially breaks R-symmetry

8. 8 Soft Terms  We take K coincident D7-branes with Kuperstein embedding:  Let us calculate the leading contribution to the gaugino mass  (3,0) RR flux leads to gaugino masses on D7-branes  But the anti D3-brane SUSY breaking state (DKM) does not generate (3,0) flux at leading order Graña, Camara et. al., Jockers et. al.  SUSY-breaking is transmitted by a tower of KK mesons: Gaugino mass

9. 9  As a result, the lightest KK mode gets a SUSY-breaking mass shift:  The DKM solution contains (0,2) and (2,0) perturbations of the metric with:  z transforms in the adjoint representation of the gauge group. We obtain a gaugino mass at 1-loop:

10. 10 Matter soft terms  Our model realizes gaugino mediation (gauge mediation with a large number of messengers)  The direct contribution to scalar masses and A-terms is negligible Kaplan et. al., Chacko et. al.   also carries R-charge. A priori, there could be an additional contribution to the gaugino mass of the form: which is highly suppresed with respect to the previous one since  <<   Instead, they are generated by RG running

11. 11 Other scenarios: Compositeness  Natural extensionallow the position of matter to vary  Single sector SUSY breaking: some SM matter emerging as composite of a SUSY-breaking field theory Arkani-Hamed, Luty and Terning Gabella, Gherghetta and Giedt  Known field theory examples are non-calculable e.g.: SU(4)×SU(18) ×[SU(18)]  Compositeness can (partially) explain some issues about flavor physics composite

12. 12 Conclusions  It is possible to geometrize models of strongly coupled gauge mediation using confining examples of AdS/CFT with massive flavors  The flavors provide messenger mesons that lead to models of semi-direct gauge mediation  Generalizations with different positions of matter fields inside the throat. Composite models with single sector SUSY breaking  Interesting to explore the interplay of compositeness contributions to soft terms with other mediation mechanisms, e.g. possible solution to tachyonic sleptons of anomaly mediation,  /B  problem, etc Seiberg, Volansky and Wecht