Generations in Flux Compactification July 23 (wed), 2014 at YITP - PowerPoint PPT Presentation

Distribution of Number of Generations in Flux Compactification July 23 (wed), 2014 at YITP workshop Taizan Watari (Kavli IPMU) arXiv:1408.xxxx w/ A. Braun (King’s) cf. arXiv:1401.???? w/ A. Braun Y. Kimura (YITP)

flux compactification of IIB/F-theory cpx str moduli stabilized     W G GVW X (isolated minimum) X  4 ( ;" ") { } (sub)-ensemble of low- H X G energy eff. theories string landscape : theoretical foundation for “ naturalness ” Low-energy eff. theories Flux gauge group, matter repr . … algebra matter multiplicity ? topology moduli eff. coupling constants

( ,[ ], ) R: A4, D5, … unif. symmetry Specify . B S R 3 of your interest [S] : divisor class of 3 B   :moduli space of with S = “7 -brane of sym. R ” : X B 3 X X : smooth (resolved) 4-fold 1    1,1 1,1 ( ) 1 ( ) ran k( ) . h X h B R 3 1,1 h Decomposition 2,1 2,1 cf. Greene Morrison Plesser h h 1 3,1 3,1 2,2 1 h h h    4 2,2 2,2 4 ( ) ( ) ( ) ( ); H X H X H X H X V RM H 2,1 2,1 h h     4 2 ( ; ) { , , , } H X Span D D 1,1 h H X X X      4,0 3,1 2,2 1,3 4,0 . H H H H H H 1 4 ( ; ) H X cf: IIB orientifold 3-forms = H Hodge diamond of X (Denef Douglas ’04)

A.Braun , Kimura, TW ’14 • Observations A.Braun , TW ‘14 2,2 (   – Generally (be aware) ) . H X RM         • K3 x K3 2,2 (22 ) (22 ) . h 1 2 1 2 RM • toric hypersurface CY4: many examples 2,2 ( – Flux in often breaks the unif. symm. R. ) H X RM – Net chirality is generated by a flux in 2,2 ( ) H X V • because the matter surface for R=SU(5) is vertical. • We are led to a proposal of flux ensembles    4 4 { | ( )} ( ) G G G H X H X fix scan scan H controls N_gen  2,2 ( ) G H X constructed in Marsano et.al. ’11 (dual to Het) fix V

• Ashok-Denef- Douglas’ theory ( contin. approx) ’03, ‘04 vacuum index  /2 K (2 ) L    * ; . d K L density distribution * I I ( / 2)! K – K = dim[ flux scanning space ], L*= D3-tadpole. – if the prefactor becomes  * , K L exp[ 2 ]. KL * – the distribution on    R  3,1 ,     m h det 1 ,      I m m   2 2 i – if the scanning space covers all of non-verticals (Denef ’08) 4 ( ) – whenever the scanning space contains H X (Braun Kimura TW ’14) H  • #vac from the prefactor, copling distrib from I

• computation in examples A.Braun TW ‘14   [ ( )], S is the zero of B n 2 3 2 2 prelim. result. containing error  4 dim[ ( )]. K H X H  ( ) 1 ( X    2 ) L G * fix 24 2 • more generally, whenever 2,2 2,2 2,2 , . 3,1 1,1 , h h h h h H V RM      ( ) , max X K (24 ) 8 . L L K * * Gaussian distribution        /2 2 K #( ) exp[ 2 ] exp[ (4 ) ]. vac KL e cN   * gen algebraic topological •   (10) ? K K 4 5 A D ( based on K3 x K3 or the examples above)