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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

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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

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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.

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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

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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:

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

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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

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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

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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:

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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

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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

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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

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Supersymmetry and Gauge Symmetry Breaking from Intersecting Branes A. Giveon, D.K. hep-th/0703135.

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