axion and anomalous u(1) gauge symmetry axion and anomalous u(1) gauge symmetry in string theory in...
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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:
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.