Choi by huanghengdong


									Axion, anomalous U(1) gauge symmetry
         and SUSY breaking

 KC, H.P.Nilles, C.S.Shin, M.Trapletti, arXiv:1011.0999 [hep-th]
 KC, K.S.Jeong, K.I.Okumura, M.Yamaguchi, arXiv:1104.3274 [hep-ph]

                                           Kiwoon Choi (KAIST)
                                     IFT Inaugural Conference & Xmas
                                         workshop (Dec. Madrid)

Axion solution to the strong CP problem and its realization in string theory

Moduli stabilizations giving an intermediate PQ scale (with compactification
      scale around the Planck scale) and the resulting patterns of SUSY breaking:

      KKLT- type scenario and Large volume scenario with anomalous U(1) gauge

Axion solution to the strong CP problem

# Strong CP problem: Why a particular combination     of CP-violating parameters
                         is so small ?

# Axion solution based on Peccei-Quinn U(1) symmetry:

  Key features of U(1)PQ :

  * U(1)PQ is broken explicitly by the QCD anomaly.

  * Compared to the breaking by QCD anomaly, other explicit breakings should be
    highly suppressed.

  * U(1)PQ is broken spontaneously at an intermediate PQ scale
Axion solution to the strong CP problem          Peccei and Quinn

At low energy scales below vPQ, U(1)PQ is nonlinearly realized as


   Axion potential :

           = axion potential from U(1)PQ breaking by QCD anomaly

          = axion potential from other U(1)PQ breakings represented by
  Generically VQCD and VUV have a minimum at different values of axion field.

       VUV should be negligible compared to VQCD in order for   dynamically
        cancelled by the axion VEV :


Q1: What would be the origin of global PQ symmetry which is explicitly
      broken mostly by the QCD anomaly ?

  cf: Quantum gravity generically breaks global symmetry, so might result in
Astrophysical and cosmological considerations suggest

(Upper bound can be avoided by assuming that the axion misalignment in the early
 Universe is small, which might be justified by anthrophic argument, or by assuming
 that there was a late entropy production after the QCD phase transition but before
 the BBN.)

Q2: What would be the dynamical origin of the intermediate PQ scale?

 In SUSY model,        corresponds to a dynamical field (= saxion or modulus),
 so the magnitude of the PQ scale is determined by the mechanism to fix
 the saxion or modulus VEV.
 Such PQ symmetry can appear naturally in string theory.

* String theories include various type of higher-dim antisymmetric tensor (p-form:
 p=1,2,3,..) fields   with gauge symmetries parameterized by (p -1)-form        :

* For string compactification with p-dim cycle Sp in internal space, there exists a
 harmonic p-form                 which is locally an exact form, i.e. locally
                                , but not globally an exact form on Sp.

* Stringy axion :

   “U(1)PQ : a  a + constant” is locally equivalent to the gauge symmetry GC,
        but not globally equivalent.
This nonlinear U(1)PQ can be explicitly broken, but only through the effects associated
with nontrivial topology of Sp , e.g. associated with

* QCD anomaly :

 GC-invariant                                               U(1)PQ-breaking
 action                                                        by QCD anomaly

* UV instantons wrapping Sp :

If the p-cycle Sp has a relatively large volume or the UV instantons wrapping Sp
have chiral zero modes, the UV axion potential VUV can be safely ignored,
and there can be a good U(1)PQ in low energy effective theory.
PQ scale = axion decay constant

In supersymmetric compactification, stringy axion decay constant is determined
by the Kahler metric of its modulus partner:

For compactifications with compactification scale high enough to realize the 4D gauge

unification at MGUT ~ 1016 GeV , the modulus Kahler metric is typically of order unity,

and then the corresponding axion scale is of the order of 1016 GeV.
                                                            KC and Kim, Svrcek and Witten
PQ scale can be lowered in models with anomalous U(1) gauge symmetry
with small FI term.

Many string compactifications give anomalous U(1) gauge symmetry under which
stringy axion transforms nonlinearly.

4D effective lagrangian of such compactification includes

Low energy symmetries :
4D effective lagrangian:

Two axion-like fields: a1 and Arg(X)

   Physical axion: U(1)A invariant
   ( Other combination = longitudinal component of   )

Two key mass scales:

  Fayet –Iliopolous term in the D-term potential:

  Stuckelberg mass of      :
D-flat condition:

U(1)A gauge boson mass:

Decay constant of the p-form axion:

Decay constant of the physical axion:

So if                , the physical PQ scale can be well below 1016 GeV even

for string compactifications with high compactification scale ~ MPl .

In some case, this can not be achieved within a phenomenologically viable region
of moduli space:


On the other hand, it is quite common that D-brane models realized in type IIA or IIB
string theory (and some heterotic string compactifications also) allow supersymmetric
configuration with vanishing FI term .

This suggests an interesting possibility that an intermediate PQ scale is achieved by
stabilizing moduli at near the configuration with vanishing FI term.

A particularly interesting possibility is that PQ scale is generated by an interplay
between SUSY breaking effect and Planck-scale-suppressed higher dimensional
operator, so that
Moduli stabilization providing QCD axion with intermediate PQ scale.

A) KKLT-type moduli stabilization with anomalous U(1)

 Suppose that the visible sector gauge fields live on D7 branes wrapping a 4-cycle
 described by the Kahler modulus      .
Original KKLT scenario assumes that                          is stabilized by nonperturbative
effect, e.g. instantons wrapping the visible sector 4-cycle, yielding

However such scenario can not give a QCD axion solving the strong CP problem as
it gives

In fact, it is difficult to realize nonperturbative stabilization of    since chiral fermion
zero modes on the visible sector cycle typically make the nonperturbative
superpotential of        negligibly small.   Blumenhagen, Moster and Plauschinn

This is often considered to be problematic, however it is in fact desirable for
realizing the axion solution to the strong CP problem !
We then need a mechanism to stabilize           while preserving the non-linear

PQ symmetry

Anomalous U(1)A with vanishing FI term provides not only a mechanism to
stabilize        but also makes it possible to have an intermediate PQ scale.

KKLT- type model with anomalous U(1)A gauge symmetry and QCD axion :
                                                         KC, Jeong, Okumura and Yamaguchi

  * U(1)A :

                                         ( U(1)A charged matter fields)

            ( Physical U(1)PQ is a linear combination of U(1)v and U(1) A . )

 * Due to the chiral zero modes on the visible sector 4-cycle, there is no
   nonperturbative superpotential of          , so the model has a good PQ symmetry.
* Assume that compactification admits a solution with vanishing FI term:


* Kahler moduli (    ) other than the visible sector Kahler modulus      are
   stabilized by nonperturbative superpotential as in the original KKLT scenario.

* To generate an intermediate PQ scale, introduce U(1)A -charged SM-singlet
  matter fields X & Y which are stabilized by an interplay between SUSY breaking
  effects and Planck-scale-suppressed superpotential term:
 Vacuum configuration of the model:

 Intermediate PQ scale :

 SUSY breaking auxiliary components:

 Soft terms are determined by a mixed mediation of SUSY breaking with

  moduli mediation ~ anomaly mediation (      )   ~ gauge mediation (    )
B) Large Volume Scenario (LVS) with anomalous U(1):

LVS has been originally proposed to get the big hierarchy between m3/2 and MPl
through a huge compactification volume :
                                           Balasubramanian, Berglund, Conlon, Quevedo

Here we consider different scenario in which a large compactification volume is
responsible for the much milder hierarchy MGUT/MPl ~ 10-2 .

          ( local GUT model with stablized moduli )
Kahler moduli :

U(1)A :

Kahler potential and superpotential :
* Tb and Ts   are stabilized by the large volume mechanism,
                                                     Balasubramanian, Berglund, Conlon, Quevedo

       ( interplay between non-perturbative effect and alpha-prime correction )

* Tv    is stabilized by the D-term potential of U(1)A .

                                                                             Conlon and Pedro

*   SUSY breaking in the moduli and U(1)A sector :
 The PQ sector fields X and Y are stabilized by an interplay between SUSY breaking
 effects and the Planck-scale-suppressed superpotential term :

 Intermediate PQ scale:

  SUSY breaking in the PQ sector:

 Due to the no-scale structure, the SUSY breaking by                    is sequestered
 from the visible sector.

 Then, depending upon the existence of gauge messenger matter multiplets Q+Qc
 which have the Yukawa coupling                        , the model can realize
 either a D-term dominated SUSY breaking:                          KC, Nilles, Shin, Trapletti

 or a mixed D-term and gauge mediation scenario:
 Summary
   String theory provides an attractive framework to realize the axion solution
    to the strong CP problem.

   With anomalous U(1) gauge symmetry which can have vanishing FI term,
    intermediate PQ scale can be naturally achieved.

   Generating intermediate PQ scale can have interesting connection to the
    mediation of SUSY breaking, and therefore to the pattern of sparticle masses.

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