Holographic Gauge Mediation

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Holographic Gauge Mediation

• Sebastián Franco

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

• Stabilization of Weak/Planck hierachy

Supersymmetry

• Spontaneous SUSY breaking within MSSM

Squarks ligher than u-quarks
Gravity mediation
heavy (Planck scale) fields
Gauge mediation
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
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• 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 LS gt 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

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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The model

• Starting point

gravity dual with a SUSY breaking state at an
exponentially small scale
Deformed conifold with fluxes

• Dual to the following gauge theory

• Constructed from N D3-branes and M wrapped
  D5-branes at the conifold

• The D5-branes break conformal invariance and the
  theory undergoes a cascade of Seiberg dualities,
  which gradually reduces N and terminates in
  confinement.

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• Confinement is dual to a deformation of the
  conifold. At the bottom (IR) of the throat there
  is a finite 3-sphere of size

• Each step in the duality cascade reduces N by M
  units

• If N k M p (p ltlt 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-branes

Kachru, Pearson and Verlinde
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• There is a supergravity dual for this non-SUSY
  states (DKM)

DeWolfe, Kachru and Mulligan
vacuum energy

• Normalizable perturbation

spontaneous SUSY breaking
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Adding the SM 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

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

breaks R-symmetry
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Soft Terms
Gaugino mass

• 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

Graña, Camara et. al., Jockers et. al.

• But the anti D3-brane SUSY breaking state (DKM)
  does not generate (3,0) flux at leading order

• SUSY-breaking is transmitted by a tower of KK
  mesons

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• The DKM solution contains (0,2) and (2,0)
  perturbations of the metric

• As a result, the lightest KK mode gets a
  SUSY-breaking mass shift

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

• 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 ltlt m

• 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.

• Instead, they are generated by RG running

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Other scenarios Compositeness

• Natural extension

allow the position of matter to vary
composite

• Compositeness can (partially) explain some issues
  about flavor physics

• 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)
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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

Seiberg, Volansky and Wecht

• 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