The discrete beauty of local GUTs

The discrete beauty of local GUTs Hans Peter Nilles Physikalisches Institut Universität Bonn The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 1/33

Outline Bottom-up motivation for GUTs and the fate of global U(1) symmetries The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 2/33

Outline Bottom-up motivation for GUTs and the fate of global U(1) symmetries require a consistent UV-completion of the theory! string theory supplies the concept of local grand unification discrete symmetries moduli stabilization and Susy breakdown gaugino condensation and uplifting gravity and mirage mediation The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 2/33

GUT evidence Experimental findings suggest the existence of two new scales of physics beyond the standard model M GUT 10 16 GeV and M SUSY 10 3 GeV: The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 3/33

GUT evidence Experimental findings suggest the existence of two new scales of physics beyond the standard model M GUT 10 16 GeV and M SUSY 10 3 GeV: Neutrino-oscillations and See-Saw Mechanism m ν M 2 W /M GUT m ν 10 3 ev for M W 100GeV, The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 3/33

GUT evidence Experimental findings suggest the existence of two new scales of physics beyond the standard model M GUT 10 16 GeV and M SUSY 10 3 GeV: Neutrino-oscillations and See-Saw Mechanism m ν M 2 W /M GUT m ν 10 3 ev for M W 100GeV, Evolution of couplings constants of the standard model towards higher energies. The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 3/33

MSusySM = MSSM The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 4/33

Standard Model The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 5/33

The fate of global symmetries Global U(1) symmetries are very useful for absence of FCNC (solve flavour problem) Yukawa textures à la Frogatt-Nielsen solutions to the µ problem axions and the strong CP-problem R-symmetry and proton stability The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 6/33

The fate of global symmetries Global U(1) symmetries are very useful for absence of FCNC (solve flavour problem) Yukawa textures à la Frogatt-Nielsen solutions to the µ problem axions and the strong CP-problem R-symmetry and proton stability But they might be destroyed by gravitational effects: we need a UV-completion with consistent incorporation of gravity The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 6/33

String theory as a UV-completion What do we get from string theory? supersymmetry extra spatial dimensions (large unified) gauge groups consistent theory of gravity many discrete symmetries The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 7/33

String theory as a UV-completion What do we get from string theory? supersymmetry extra spatial dimensions (large unified) gauge groups consistent theory of gravity many discrete symmetries String theory could serve as the UV-completion with a consistent incorporation of gravity, but we need to make contact with the real world (MSSM). The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 7/33

Strings versus GUTs There is some tension between GUTs and strings intersecting branes in type IIA,B F-theory The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 8/33

F-theory (cum grano salis) The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 9/33

Strings versus GUTs There is some tension between GUTs and strings intersecting branes in type IIA,B F-theory heterotic string The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 10/33

Strings versus GUTs There is some tension between GUTs and strings intersecting branes in type IIA,B F-theory heterotic string There remain some corners that are compatible with a grand unified desert a variant of the GUT picture (local GUTs) consistent incorporation of MSSM (Lebedev, HPN, Raby, Ramos-Sanchez, Ratz, Vaudrevange, Wingerter, 2007) The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 10/33

Local Grand Unification In fact string theory gives us a variant of GUTs complete multiplets for fermion families split multiplets for gauge- and Higgs-bosons partial Yukawa unification The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 11/33

Local Grand Unification In fact string theory gives us a variant of GUTs complete multiplets for fermion families split multiplets for gauge- and Higgs-bosons partial Yukawa unification Key properties of the theory depend on the geography of the fields in extra dimensions. This geometrical set-up called local grand unification, can be realized in the framework of the heterotic braneworld. (Förste, HPN, Vaudrevange, Wingerter, 2004; Buchmüller, Hamaguchi, Lebedev, Ratz, 2004) The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 11/33

Localized gauge symmetries SU(4) 2 SU(6) SU(2) SO(10) SU(6) SU(2) The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 12/33

Standard Model Gauge Group SU(4) 2 SU(4) SU(2) 2 SU(5) SU(3) 2 SU(3) 2 SU(6) SU(2) SO(10) SU(5) SU(4) SU(2) 2 SU(6) SU(2) The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 13/33

The Heterotic Braneworld 300 models with the exact spectrum of the MSSM (absence of chiral exotics) (Lebedev, HPN, Raby, Ramos-Sanchez, Ratz, Vaudrevange, Wingerter, 2007-2009) local grand unification (by construction) gauge- and (partial) Yukawa unification examples of neutrino see-saw mechanism (Raby, Wingerter, 2007) (Buchmüller, Hamguchi, Lebedev, Ramos-Sanchez, Ratz, 2007) models with R-parity + solution to the µ-problem (Lebedev, HPN, Raby, Ramos-Sanchez, Ratz, Vaudrevange, Wingerter, 2007) gaugino condensation and mirage mediation (Löwen, HPN, 2008) The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 14/33

Symmetries String theory gives us gauge symmetries discrete global symmetries from geometry and stringy selection rules (Kobayashi, HPN, Plöger, Raby, Ratz, 2006) accidental global U(1) symmetries in the low energy effective action (Choi, Kim, Kim, 2006; Choi, HPN, Ramos-Sanchez, Vaudrevange, 2008) The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 15/33

Location matters The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 16/33

Symmetries String theory gives us gauge symmetries discrete global symmetries from geometry and stringy selection rules (Kobayashi, HPN, Plöger, Raby, Ratz, 2006) accidental global U(1) symmetries in the low energy effective action (Choi, Kim, Kim, 2006; Choi, HPN, Ramos-Sanchez, Vaudrevange, 2008) We might live close to a fixed point with enhanced symmetries that explain small parameters in the low energy effective theory. The symmetries can be trusted as we are working within a consistent theory of gravity. The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 17/33

Applications of global symmetries Applications of discrete and accidental global symmetries: (nonabelian) family symmetries (and FCNC) (Ko, Kobayashi, Park, Raby, 2007) Yukawa textures (via Frogatt-Nielsen mechanism) a solution to the µ-problem (Lebedev, HPN, Raby, Ramos-Sanchez, Ratz, Vaudrevange, Wingerter, 2007) creation of hierarchies (Kappl, HPN, Ramos-Sanchez, Ratz, Schmidt-Hoberg, Vaudrevange, 2008) proton stability via Proton Hexality (Dreiner, Luhn, Thormeier, 2005; Förste, HPN, Ramos-Sanchez, Vaudrevange, 2010) approximate global U(1) for a QCD accion (Choi, Kim, Kim, 2006; Choi, HPN, Ramos-Sanchez, Vaudrevange, 2008) The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 18/33

A Benchmark Model At the orbifold point the gauge group is SU(3) SU(2) U(1) 9 SU(4) SU(2) one U(1) is anomalous there are singlets and vectorlike exotics decoupling of exotics and breakdown of gauge group has been verified remaining gauge group SU(3) SU(2) U(1) Y SU(4) hidden for discussion of neutrinos and R-parity we keep also the U(1) B L charges The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 19/33

Spectrum # irrep label # irrep label `3,1;1,1 3 (3,2;1,1) (1/6,1/3) q i 3 ( 2/3, 1/3) 3 (1,1;1,1) (1,1) ē i 8 (1,2;1,1) (0, ) m i `3,1;1,1 3 + 1 d i 1 (3,1;1,1) ( 1/3,1/3) d i (1/3, 1/3) 3 + 1 (1,2;1,1) ( 1/2, 1) l i 1 (1,2;1,1) (1/2,1) li 1 (1,2;1,1) ( 1/2,0) h d 1 (1,2;1,1) (1/2,0) h u `3,1;1,1 6 δ i 6 (3,1;1,1) ( 1/3, 2/3) δ i (1/3,2/3) 14 (1,1;1,1) (1/2, ) s + i 14 (1,1;1,1) ( 1/2, ) s i 16 (1,1;1,1) (0,1) n i 13 (1,1;1,1) (0, 1) n i 5 (1,1;1,2) (0,1) η i 5 (1,1;1,2) (0, 1) η i 10 (1,1;1,2) (0,0) h i 2 (1,2;1,2) (0,0) y i `1,1;4,1 6 (1,1;4,1) (0, ) f i 6 f (0, ) i 2 (1,1;4,1) ( 1/2, 1) f `1,1;4,1 i 2 (1/2,1) 4 (1,1;1,1) (0,±2) χ i 32 (1,1;1,1) (0,0) s 0 i `3,1;1,1 2 v i 2 (3,1;1,1) (1/6, 2/3) v i ( 1/6,2/3) ū i f + i The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 20/33

Unification 0.09 Higgs doublets are in untwisted (U3) sector trilinear coupling to the top-quark allowed heavy top quark Αi 0.08 0.07 0.06 0.05 0.04 0.03 0.02 Α 3 Α t Α 2 Α 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 log 10 Μ GeV threshold corrections ( on third torus ) allow unification at correct scale around 10 16 GeV natural incorporation of gauge-yukawa unification (Hosteins, Kappl, Ratz, Schmidt-Hoberg, 2009) The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 21/33

Hidden Sector Gaugino Condensation 25 # of models 20 15 10 5 0 2 4 6 8 10 12 14 16 log 10 GeV Gravitino mass m 3/2 = Λ 3 /M 2 Planck and Λ exp( S) (Lebedev, HPN, Raby, Ramos-Sanchez, Ratz, Vaudrevange, Wingerter, 2006) The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 22/33

Dilaton (Modulus) Domination This leads to a variant the gravity mediation scenario, but we still have to adjust the vacuum energy. Here we need a downlifting mechanism: downlifting mechanism can fix S as well (no need for nonperturbative corrections to the Kähler potential) gives a suppression factor log(m 3/2 /M Planck ) mirage mediation for gaugino masses (Löwen, HPN, 2008) (Choi, Falkowski, HPN, Olechowski, 2005) The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 23/33

Evolution of couplings Αi 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 log 10 Μ GeV The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 24/33

Mirage Scale Α 1 m 3 2 20 TeV Φ 0 1.2 1 M 1 Mass TeV 0.8 M 2 0.6 0.4 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 Μ GeV M 3 The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 25/33

The Gaugino Code Mixed boundary conditions at the GUT scale characterized by the parameter α: the ratio of modulus to anomaly mediation. M 1 : M 2 : M 3 1 : 2 : 6 for α 0 M 1 : M 2 : M 3 1 : 1.3 : 2.5 for α 1 M 1 : M 2 : M 3 1 : 1 : 1 for α 2 M 1 : M 2 : M 3 3.3 : 1 : 9 for α The mirage scheme leads to LSP χ 0 1 predominantly Bino a compact gaugino mass pattern. (Choi, HPN, 2007; Löwen, HPN, 2009) The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 26/33

Gaugino Masses 3 Ma M0 1 Α 2 1 2 2 1 0 1 2 Modulus M 3 M 2 M 1 Anomaly 3 0 1 2 3 5 10 Α The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 27/33

Scalar Masses 1.5 L q L 1 e R m i 2 M 0 2 1 Α 2 0.5 Modulus Anomaly 0 0.5 0 1 2 3 5 10 Α The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 28/33

Scalar Masses 0.7 0.6 0.5 q L m i 2 M 0 2 1 Α 2 0.4 0.3 0.2 Modulus L Anomaly 0.1 e R 0 0.1 0 1 2 3 5 10 Α The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 29/33

Constraints on α tanβ 30 Ξ 1 3 Φ 0 60 50 t LSP 40 TACHYONS m3 2 TeV 30 20 WMAP 10 0 Below LEP 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 Α The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 30/33

Constraints on α (modified mirage) tanβ 30 Η i 3 60 m3 2 TeV 50 40 30 20 10 t LSP Χ LSP g LSP No EWSB Χ LSP 0 Below LEP Below LEP 0 1 2 3 4 5 6 7 8 Α The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 31/33

Conclusion String theory might provide us with a consistent UV-completion of the MSSM inchluding Local Grand Unification Accidental symmetries (of discrete origin) Geography of extra dimensions plays a crucial role: gauge-yukawa unification and a naturally heavy top gravity-mirage mediation without a flavour problem We seem to live at a special place in the extra dimensions! The LHC might clarify the case for (local) grand unification. The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 32/33

Where do we live? The discrete beauty of local grand unification, GUTs and Strings, MPI München, February 2010 p. 33/33