1. 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) TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAA A A A A AA A A A A

2. 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

3. Axion solution to the strong CP problem * Strong CP problem: Why is so small ? * Axion solution based on PQ symmetry:

4. Axion solution to the strong CP problem Peccei and Quinn

5. If explicit PQ-breakings other than the QCD anomaly are highly suppressed, so that then V QCD 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 )

6. 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, f a is a dynamical field (= saxion or modulus), and then the axion scale is determined by the mechanism to fix the saxion VEV (saxion stabilization).

7. 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 S p 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 G C, but not globally:

8. U(1) PQ can be explicitly broken, but only through the effects associated with the global topology of S p, in particular with * QCD anomaly: G C -invariant   U(1) PQ -breaking action by QCD anomaly * UV instantons wrapping S p : So, if the internal closed surface S p has a large volume, e.g. Vol (S p ) > O(100), the higher dim gauge symmetry G C 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

9. Axion scale Axion decay constant in supersymmetric compactification: ~ 10 -1 x compactification scale Typically compactification scale is somewhat close to M Pl, so the modulus (saxion) Kahler metric is of order unity, and then the string theory axion scale is of the order of 10 16 GeV. KC and Kim, Svrcek and Witten

10. 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:

11. Low energy symmetries: Two axion-like fields: a 1 and Arg(X) Physical axion: U(1) A invariant (other combination = longtidinal component of ) Two key mass scales: Fayet –Iliopolous term: Stuckelberg mass:

12. 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: 

13. 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

14. Moduli stabilization and SUSY breaking In string theory, all mass scales (in unit with M string = 1) are determined by the mechanism of moduli stabilization. Example: Scales in (a variant of) KKLT-type moduli stabilization ( ) SUSY breaking scale:

15. Fine-tuning for vanishing cosmological constant:  ( ( ) Closed 4-dim surfaces wrapped by D7 branes supporting gauge and matter fields: ( Only a 1 can be a candidate for the QCD axion. ) KKLT assume that T 1 = t 1 + ia 1 and T 2 = t 2 + ia 2 are stabilized by nonperturbative effects, e.g. instantons wrapping the corresponding 4-dim surfaces, which are encoded in the superpotential

16. 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 A 1 = 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 t 1. Anomalous U(1) A with vanishing FI term provides not only a mechanism to stabilize t 1, but also makes it possible to have an intermediate QCD axion scale. KC, Jeong, Okumura and Yamaguchi

17. Anomalous U(1) A gauge symmetry: * Physical U(1) PQ is a linear combination of U(1) T1 and U(1) A. * Q+Q c corresponds to the heavy quark in KSVZ axion model. Kahler potential and and superpotential: * Assume that compactification admits configuration with vanishing FI term:

18. 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

19.  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.