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) Outline 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 symmetry Conclusion 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: Example: 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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