Axion and anomalous U(1) gauge symmetry Axion and anomalous U(1) gauge symmetry in string theory in string theory

Kiwoon Choi (KAIST)

ASK 2011

Apr.11 – 12, 2011 (SNU)

Outline

Axion solution to the strong CP problem

Origin of PQ symmetry

* Higher-dim gauge symmetry for antisymmetric tensor gauge field

as the origin of U(1)PQ string theory axion

* Intermediate axion scale with anomalous U(1) gauge symmetry

Connection to moduli stabilization and SUSY breaking

Conclusion

Axion solution to the strong CP problem

* Strong CP problem: Why is so small ?

* Axion solution based on PQ symmetry:

Axion solution to the strong CP problem Peccei and Quinn

If explicit PQ-breakings other than the QCD anomaly are highly suppressed, so that

then VQCD derives the axion VEV to cancels regardless of the value

of

Q1: What would be the origin of such global symmetry explicitly

broken in a very peculiar way?

(cf: Quantum gravity generically breaks global symmetry, which would

result in )

Astrophysical and cosmological considerations suggest

(Upper bound can be avoided by assuming that the axion misalignment in

the early Universe is small, or there is a late entropy production.)

Q2: What would be the dynamical origin of the spontaneous

PQ breaking at an intermediate scale?

In SUSY model, fa is a dynamical field (= saxion or modulus), and then

the axion scale is determined by the mechanism to fix the saxion VEV

(saxion stabilization).

Higher dim gauge symmetry as the origin of U(1)PQ

* Antisymmetric tensor (p-form: p=1,2,3,…) gauge field:

* p-dim closed but non-contractible surface Sp in internal space

curl-free but not exact p-form

locally

but not globally, so

* Axion:

U(1)PQ is locally equivalent to the gauge symmetry GC, but

not globally:

U(1)PQ can be explicitly broken, but only through the effects associated with the global topology of Sp , in particular with

* QCD anomaly:

GC-invariant U(1)PQ-breaking

action by QCD anomaly

* UV instantons wrapping Sp :

So, if the internal closed surface Sp has a large volume, e.g.

Vol (Sp) > O(100) , the higher dim gauge symmetry GC can give rise to

a good U(1)PQ in low energy theory.

This setup is most naturally realized in string theory. String theory axion

Axion scale

Axion decay constant in supersymmetric compactification:

~ 10-1 x compactification scale

Typically compactification scale is somewhat close to MPl , so the modulus

(saxion) Kahler metric is of order unity, and then the string theory axion scale

is of the order of 1016 GeV. KC and Kim, Svrcek and Witten

Axion scale with anomalous U(1) gauge symmetry

Anomalous U(1) gauge symmetry under which stringy axion transforms

nonlinearly appears quite often.

Example: Axion from self-dual 4-form gauge field

Axion fluctuation:

Low energy symmetries:

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

Physical axion: U(1)A invariant (other combination = longtidinal component of )

Two key mass scales: Fayet –Iliopolous term:

Stuckelberg mass:

D-flat condition:

U(1)A gauge boson mass:

Decay constant of the 4-form axion:

Physical axion scale:

In some case, , and then U(1)A is not useful for lowering the

axion scale.

Example:

On the other hand, it is quite common that D-brane models realized in

type IIA or IIB string theory allow supersymmetric moduli configuration

with vanishing FI-term.

This suggests an interesting possibility that an intermediate axion scale arises as a consequence of stabilizing moduli at near the configuration with vanishing FI term.

In such scenario, the moduli and matter fields might be stabilized by SUSY breaking effects at

Kim and Nilles

Kim and Nilles

Moduli stabilization and SUSY breaking

In string theory, all mass scales (in unit with Mstring = 1) are determined by

the mechanism of moduli stabilization.

Example: Scales in (a variant of) KKLT-type moduli stabilization

( )

SUSY breaking scale:

Fine-tuning for vanishing cosmological constant:

( ( )

Closed 4-dim surfaces wrapped by D7 branes supporting gauge and matter fields:

( Only a1 can be a candidate for the QCD axion. )

KKLT assume that T1 = t1 + ia1 and T2 = t2 + ia2 are stabilized by

nonperturbative effects, e.g. instantons wrapping the corresponding 4-dim

surfaces, which are encoded in the superpotential

This is good for moduli stabilization, but no axion for the strong CP problem:

However chiral fermion zero modes on the visible sector surface generically make A1 = 0 . Blumenhagen, Moster and Plauschinn

This would be good for the strong CP problem,

global U(1)T1 originating from 4-form gauge symmetry, which is

dominantly broken by the QCD anomaly:

U(1) T1 :

but requires a separate mechanism to stabilize t1 .

Anomalous U(1)A with vanishing FI term provides not only a mechanism to stabilize t1, but also makes it possible to have an intermediate QCD axion

scale. KC, Jeong, Okumura and Yamaguchi

Anomalous U(1)A gauge symmetry:

* Physical U(1)PQ is a linear combination of U(1)T1 and U(1)A.

* Q+Qc corresponds to the heavy quark in KSVZ axion model .

Kahler potential and and superpotential:

* Assume that compactification admits configuration with vanishing FI term:

Minimizing the scalar potential,

* intermediate axion scale:

* SUSY breaking:

Connection to sparticle (gaugino/sfermion) masses:

Gauge mediation ~ Anomaly mediation ~ Modulus mediation

Deflected mirage mediation with distinctive pattern of sparticle masses (PQ sector = messenger of gauge mediation)

KC, Falkowski, Nilles, Olechowski; Everett, Kim, Ouyang, Zurek

Summary

Higher dim p-form gauge symmetry in string theory might be the origin

of U(1)PQ solving the strong CP problem in low energy effective theory.

Anomalous U(1) gauge symmetry with vanishing FI term provides an

attractive setup for intermediate axion scale in string theory.

Generating an intermediate axion scale by SUSY breaking effects have

implications to sparticle masses which might be tested at the LHC.