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Asymmetric Orbifold toward Heterotic Anomalous U(1) GUT

Asymmetric Orbifold toward Heterotic Anomalous U(1) GUT. Toshifumi Yamashita (Nagoya University). 09 Nov. 2009 @KEK mini workshop. working with Nagoya U. : Maekawa, Moriyama, Teraguchi Takei, Ito, Kuwakino NCTU (Taiwan) : Keijiro Takahashi.

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Asymmetric Orbifold toward Heterotic Anomalous U(1) GUT

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  1. Asymmetric OrbifoldtowardHeterotic Anomalous U(1) GUT Toshifumi Yamashita (Nagoya University) 09 Nov. 2009@KEK mini workshop working with Nagoya U. : Maekawa, Moriyama, Teraguchi Takei, Ito, Kuwakino NCTU (Taiwan) :Keijiro Takahashi

  2. Introduction • anomalous U(1) GUT N. Maekawa&T.Y. & ・・・ (’01-’04) • an interesting SUSY-GUT e.g. E6*SU(2)H DTS, PD, Yukawa hierarchy, SUSY flavor etc. • anomaly : assumed to be cancelled by GS. to be checked We aim to embed it into string. Asymmetric orbifold • GUTs from the Heterotic string. • examined in '80 exhaustively simple cpt. no adjoint Higgs Kac-Moody level

  3. Plan • Introduction • anomalous U(1) GUT • overview • Narain cpt. & Modular inv. & orbifold • Models • Summary

  4. : non-Abelian Grand Unified Theories • Unification of Gauge Group Charge Quantization • Unification of Matter SU(5) SO(10) E6 + + = + + = wrong GUT relation

  5. Grand Unified Theories • sector in E6 model • E-twisting M.Bando and T.Kugo mass massless : • mildhierarchy in sector !! • all come from and . large mixing

  6. : non-Abelian Grand Unified Theories • Unification of Gauge Group Charge Quantization • How about Higgs ? Proton decay Doublet-Triplet (DT) Splitting Problem

  7. SUSY, (FCNC)? SUSY-GUT hierarchal Yukawa? • unifications of forces and of matter • charge quantization • stabilization of the weak scale • gauge coupling unification (GCU) • fascinating extension of SM Higgs? Proton decay?

  8. : FN field : cutoff scale Anomalous U(1) gauge symmetry • Low energy theory of string theory • Anomaly Green-Schwartz mechanism • Froggatt-Nielsen (FN) mechanism ex)

  9. does not appear in . This strongly constrain !! Anomalous U(1) gauge symmetry • Low energy theory of string theory • Anomaly Green-Schwartz mechanism • Froggatt-Nielsen (FN) mechanism • SUSY-zero (holomorphic-zero) mechanism superpotential : holomorphic Only positively charged operators can appear.

  10. Anomalous U(1) gauge symmetry • Low energy theory of string theory • Anomaly Green-Schwartz mechanism • Froggatt-Nielsen (FN) mechanism • SUSY-zero (holomorphic-zero) mechanism Adjoints of SO(10) : Ex) Only the linear terms in A’ are relevant for EOM.

  11. Anomalous U(1) gauge symmetry • Low energy theory of string theory • Anomaly Green-Schwartz mechanism • Froggatt-Nielsen (FN) mechanism • SUSY-zero (holomorphic-zero) mechanism Adjoints of SO(10) : Ex) The # of non-zero xi labels the vacuum N=3 : Dimopoulos-Wilczek VEV DTS

  12. Anomalous U(1) GUT N.Maekawa & T.Y. & … SUSY-GUT w/ anomalous U(1) symmetry • Ansatz • “generic” interaction introduce allpossible interactions (including NROs) assume all the coefficients are O(1) • vacuum (cutoff scale) : GUT singlet operator, : U(1)A charge : breaking scale of U(1)A charge assignment ＝ def. of model

  13. Anomalous U(1) GUT N.Maekawa & T.Y. & … • Generic interaction • FN mechanism • SUSY-zero mechanism • Natural Gauge Coupling Unification hierarchal Fermion Yukawa DW type of adjoint VEV DT Splitting proton decay GCU

  14. horizontal symm. SUSY, (FCNC)? Anomalous U(1) GUT N.Maekawa & T.Y. & … hierarchal Yukawa? • fascinating extension of SM • unifications of forces and of matter • charge quantization • stabilization of the weak scale • gauge coupling unification (GCU) Higgs? Proton decay? Almost all the problem can be solved!!

  15. Anomalous U(1) GUT N.Maekawa & T.Y. & … • examples of E6 model PTP 107, 1201 (2002) N.Maekawa and T.Y. E6 * Z2 PLB561, 273(2003) N.Maekawa two charged adjoint 6 – 3 or 5 – 2 generations E6 * SU(2)

  16. Plan • Introduction • anomalous U(1) GUT • overview • Narain cpt. & Modular inv. & orbifold • Models • Summary

  17. asymmetric orbifold overview anomalous U(1) GUT -- E6 model charged adjoint Higgs higher Kac-Moody level Het, M, F, … related to doubled geometry? diagonal embedding -- Narain cpt. • asymmetric treatment of left- and right-moving string need careful consistency check

  18. : structure constant w/ overview • Kac-Moody algebra ex) mode exp. of world sheet current • Diagonal embedding

  19. Only one model is possible. overview • # of generation e.g. J.Erler (1996) (in known models) Z.Kakushadze &H.Tye (1996) • model cpt. of or SO(32) Hetero w/ Wilson line Z.Kakushadze &H.Tye (1996) claimed w/ adjoint Higgs, 3 generations & non-Abelian Hidden gauge Narain compactification (flat instead of CY, for simplicity)

  20. Plan • Introduction • anomalous U(1) GUT • overview • Narain cpt. & Modular inv. & orbifold • Models • Summary

  21. Narain cpt. & Modular inv. & orbifold • string w/ compactification

  22. 4D 6D 16D on or Spin(32)/Z2 Lie lattice left right Narain cpt. & Modular inv. & orbifold • Heterotic string from modular inv. "compactified" here? no geometrical interpretation • Narain compactification discard geometric interpretation also in cpt. 6D gauge symm w/ rank 22 is possible : ex)

  23. red blue shift Narain cpt. & Modular inv. & orbifold • Modular invariance The modular transformations, closed string 1-loop amp. do not change the torus. The amplitude should be invariant under these tr..

  24. Narain cpt. & Modular inv. & orbifold • partition function : NS : R

  25. (or ) Narain cpt. & Modular inv. & orbifold • partition function even T S self-dual

  26. Narain cpt. & Modular inv. & orbifold • geometric compactification ex.) A2 lattice winding momentum This momentum lattice is actually even & self-dual. proof

  27. Narain cpt. & Modular inv. & orbifold • Narain lattice Cf.) geometric : simple roots of a (simply laced) Lie group. winding momentum • R=1 21/2 ( ; 0) • R= 2-1/2 for pR=0 : Cartan matrix This lattice leads to gauge symmetry. This does not, except for SU(2).

  28. Narain cpt. & Modular inv. & orbifold • ESDL generating technique left right

  29. Narain cpt. & Modular inv. & orbifold • ESDL generating technique more left right left right

  30. Narain cpt. & Modular inv. & orbifold ZNfor simplicity • orbifold diagonal embedding 4D N=1 SUSY Manifold / discrete symm. impose identity under (discrete) orbifold action twist (rotation) shift (reflection) : Z2,3,6 ex.) A2 lattice 1/3twist : does not change the lattice

  31. Narain cpt. & Modular inv. & orbifold ZNfor simplicity • orbifold diagonal embedding 4D N=1 SUSY Manifold / discrete symm. impose identity under (discrete) orbifold action twist (rotation) shift (reflection) : Z2,3,6 ex.) A2 lattice additional string states : does not change the lattice

  32. S S T Narain cpt. & Modular inv. & orbifold • partition function additional string state w/ different B.C. • Modular tr. S2=1

  33. T : S : Narain cpt. & Modular inv. & orbifold • partition function ex) Z3 S • Modular tr. S S2=1 T

  34. T : S : Rules on are established for symm. orbifold. Narain cpt. & Modular inv. & orbifold • partition function ex) Z3 • Modular inv. P.F. is inv. if each sector satisfies the tr. property. Z.Kakushadze &H.Tye (1996) For asymm. orbifold, not yet.

  35. T : S : Narain cpt. & Modular inv. & orbifold • partition function ex) Z3 • Modular inv. We make and then define by S, T.

  36. T : S : Narain cpt. & Modular inv. & orbifold • partition function ex) Z3 • Modular inv. The remaining S, T give non-trivial conditions.

  37. Plan • Introduction • anomalous U(1) GUT • overview • Narain cpt. & Modular inv. & orbifold • Models • Summary

  38. 4D N=1 SUSY even Models • 4D SUSY 4D left right zero modes SO(8)LC repr. phase

  39. Models • diagonal embedding : Z3 4D E6 E6 E6 combined with phaseless RM to form gauge field. left right level 3 E6

  40. 4D N=1 SUSY Models • lattice for right-mover 4D left right : Z3 E6 A2 A2 A2 D4 A2

  41. Models • possible models 4D Z.Kakushadze &H.Tye (1996) A2 A2 E6 E6 E6 left E6 right 1 neutral adj. 5 – 2 generations Z6 A2 A2 E6 E6 E6 A2 A2 A2 Z6 : vector-like Z3 : 9 generations D4 E6 E6 E6 D4 A2

  42. Summary • We are working on Heterotic GUTs to derive Anomalous U(1) GUT from string. • to get 4D N=1 SUSY E6 model w/ adjoint Higgs & 3 generations E63 lattice via Narain compactification diagonal embedding in asymmetric orbifold • Future works We want two charged Adjoint Higgs towards Anomalous U(1) GUT

  43. Back-up Slides

  44. Narain cpt. & Modular inv. & orbifold • ESDL generating technique (248) (78,1)+(1,8)+[(27,3)+c.c.] (78;1)+(1;78)+[(27;27)+c.c.] left (78;1,1,1)+(1;8,1,1)+[(1;3,3,3)+c.c.] +[(27;3,3,1)+c.c.] right (78,1,1;1)+(1,1,1;8)+[(1,27,27;3)+c.c.] +[(27,27,27;1)+(27,1,27;3)+(27,27,1;3) +(27,27,27;1)+(27,1,27;3)+(27,27,1;3)] left right

  45. Narain cpt. & Modular inv. & orbifold • ESDL generating technique (248) (78,1)+(1,8)+[(27,3)+c.c.] (78;1)+(1;78)+[(27;27)+c.c.] left (78;1,1,1)+(1;8,1,1)+[(1;3,3,3)+c.c.] +[(27;3,3,1)+c.c.] right (78,1,1;1)+(1,1,1;8)+[(1,27,27;3)+c.c.] +[(27,27,27;1)+(27,1,27;3)+(27,27,1;3) +(27,27,27;1)+(27,1,27;3)+(27,27,1;3)] left right

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