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

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Motivation

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Stabilization of Weak/Planck hierachy Supersymmetry

Spontaneous SUSY breaking within MSSM Squarks ligher than u-quarks

SUSY MSSM

Hidden Visible

SUSY MSSM

Hidden Visible

Mediation

Gravity mediation

Gauge mediation

heavy (Planck scale) fields

massive fields with SM charges

Minimal Gauge MediationMinimal 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

MessengersMessengers:: ( charged under SM

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Today: new possibilities that are calculable via gauge/gravity duality

VisibleVisible:: SUSY extension of the SM. We assume visible, hidden and messenger matter in complete SU(5) representations.

HiddenHidden:: 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 Jh 2-point functions Meade, Seiberg and Shih

Geometrization: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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Starting point: gravity dual with a SUSY breaking state at an exponentially small scale

The model

Deformed conifold with fluxesDeformed 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

SU(N+M)

B1,2

A1,2

SU(N)

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If N = k M – p (p << M), we are left with (M-p) probe D3-branes at the S3 at the tip of the deformed conifold

The theory admits a metastable state with p anti D3-branesKachru, Pearson and Verlinde

M-p D3

S3

(a)

p D3

S3

(b)

M-p D3

S3

(a)V

f

(b)

(a)M-p D3

S3

(a)

p D3

S3

(b)

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 Normalizable perturbation spontaneous SUSY breaking

There is a supergravity dual for this non-SUSY states (DKM):DeWolfe, Kachru and Mulligan

vacuum energy

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global symmetry in 4d gauge 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

D3

e

K D7 SU(K) SU(5)

m

SU(N+M)

B1,2

A1,2

SU(N) SU(K) SU(5)

c

c

In type IIB, this is achieved with a stack of D7-branes extending radially

breaks R-symmetry

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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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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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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 negligibleKaplan et. al., Chacko et. al.

e 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 e << m

Instead, they are generated by RG running

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Other scenarios: Compositeness Natural extension allow the position of matter to vary

Single sector SUSY breakingSingle sector SUSY breaking:: some SM matter emerging as composite of a SUSY-breaking field theoryArkani-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

D3 SU(5)

rUV

1st, 2nd, 3rd, H

D3 SU(5)

H3rd1st, 2nd

composite

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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, m/Bm problem, etc

Seiberg, Volansky and Wecht