The F-ate of GUTs Sakura Sch afer-Nameki Seminar at DAMTP, - PowerPoint PPT Presentation

The F-ate of GUTs Sakura Sch¨ afer-Nameki Seminar at DAMTP, Cambridge, March 3, 2011 Joe Marsano, Natalia Saulina, SS-N 0808.1286 , 0808.1571 , 0808.2450 , 0904.3932 , 0906.4672 , 0912.0272 , 1006.0483 , WIP 2 and with Matt Dolan 1102.0290, WIP

Two Key Questions in String Phenomenology Is there any realistic particle physics within string theory? Is there an imprint of the UV completion(s) upon the low energy physics?

Three-Step Strategy Is there any realistic particle physics within string theory? Step 1: Low energy gauge dof’s decoupling gravity dof’s M GUT M Pl ∼ 10 − 3 : SU (5) SUSY GUT, SUSY-breaking, flavour, neutrino physics, etc. [Aldazabal, Ibanez, Quevedo, Uranga]

Three-Step Strategy Is there any realistic particle physics within string theory? Step 1: Low energy gauge dof’s decoupling gravity dof’s M GUT M Pl ∼ 10 − 3 : SU (5) SUSY GUT, SUSY-breaking, flavour, neutrino physics, etc. Is there an imprint of the UV completion(s) upon the low energy physics? Step 2: Global consistency and embeddability ⇒ Constraints on low energy theory ⇒ Impact on: spectrum, flavour structure

Three-Step Strategy Is there any realistic particle physics within string theory? Step 1: Low energy gauge dof’s decoupling gravity dof’s M GUT M Pl ∼ 10 − 3 : SU (5) SUSY GUT, SUSY-breaking, flavour, neutrino physics, etc. Is there an imprint of the UV completion(s) upon the low energy physics? Step 2: Global consistency and embeddability ⇒ Constraints on low energy theory ⇒ Impact on: spectrum, flavour structure Step 3: Construction of full-fledged string compactifications • Algebraic geometry gymnastics • Moduli stabilization

Three-Step Strategy with F-theory Step 1. Ultra-local Models: ⇒ Effective field theory on 7-branes: SU (5) GUT Step 2. Semi-local Model: Impose general conditions for embedding into local CY4 ⇒ Embeddability implies strong phenomenological restrictions Step 3. Global Model: Construction of elliptically fibered CY4 realizing semi-local models

Bottom-up Three-Step Strategy Step 3: Step 2: Step 1: Global Model: Semi-local Model: Local Model: Effective field theory Embeddability Compact Geometry on D-branes: ⇒ strong pheno + Fluxes SU (5) GUT restrictions

Why care? LHC is excluding more and more of the CMSSM parameter space 3000 CMSSM pa ra m e te r spa cewithta n Β 3, A 0 0 a llowe d 2.5 1000 e xclude dby LHC 2.0 V ssinGe 300 1.5 0 Μ m a e xclude dby LEP gluinom 1.0 100 0.5 0.0 30 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 M 1 2 Μ 10 na tura lne ssproba bility Strumia 1101.2195 NB: there is a tiny white sliver of allowed parameter space.

References Step 1. Ultra-local Models: [Donagi, Wijnholt], [Beasley, Heckman, Vafa]: GUTs [Marsano, Saulina, SS-N ], [Heckman, Marsano, Saulina, SS-N, Vafa]: SUSY-breaking [Heckman, Vafa + Bouchard, Cecotti, Cheng, Seo, Tavanfar,... ], [Watari, Tatar + Hayashi, Kawano, Toda, Tsuchiya, Yamazaki]: : Cosmology, Neutrinos, Flavour. Step 2. Semi-local Model: [Hayashi, Kawano, Tatar, Watari], [Donagi, Wijnholt]: spectral cover [Marsano, Saulina, SS-N]: spectral cover, phenomenological constraints from semi-local models Step 3. Global Model: [Marsano, Saulina, SS-N]: compact geometry for F-theory GUTs [Blumenhagen, Grimm, Jurke, Weigand], [Cordova]: other examples

Outline 0. Bottom-up: Local, semi-local, global 1. Local F-theory GUTs 2. Constraints: anomaly cancellation and Dudas-Palti relations 3. Semi-local and Global Model • Embedding into local E 8 singularity • Monodromies • Global geometry • Survey 4. Phenomenological Implications • Gauge-mediation with non-GUT messenger sector 5. Conclusions and Outlook

1. Local Models Low energy gauge dof’s decoupling gravity dof’s M GUT M Pl ∼ 10 − 3 : SU (5) SUSY GUT • 3 generations of   Q ∼ ( 3 , 2 ) + 1 / 6 � D c ∼ ( ¯ 3 , 1 ) + 1 / 3 � U c ∼ ( ¯  3 , 1 ) − 2 / 3  ¯  , 10 M = 5 M =   L ∼ ( 1 , 2 ) − 1 / 2  E c ∼ ( 1 , 1 ) + 1 • Higgses: lifting triplets � H u ∼ ( 1 , 2 ) + 1 / 2 � H d ∼ ( 1 , 2 ) − 1 / 2 � � ¯ , 5 H = 5 H = H (3) H (3) d ∼ ( ¯ u ∼ ( 3 , 1 ) − 1 / 3 3 , 1 ) + 1 / 3 • W ∼ λ u 5 H × 10 M × 10 M + λ d ¯ 5 H × ¯ 5 M × 10 M • SUSY-breaking, flavour, neutrino physics, etc.

MSSM from Brane-intersections • Gauge dof’s from worldvolume • Matter from Brane-intersections or equivalently: Higgsing a higher rank group by adjoint vevs � φ a � : G → SU (5) × U (1) • MSSM interactions W ∼ λ u 5 H × 10 M × 10 M + λ d ¯ 5 H × ¯ 5 M × 10 M ⇒ Can get all these from Higgsing G → SU (5) × U (1) k as long as G ⊃ E 7 ⇒ Non-perturbative string theory

F-theory F-theory [Vafa][Morrison, Vafa] =Type IIB [Green, Schwarz] vacua with varying axio-dilaton: τ = C 0 + ie − φ Geometrize τ consistent with SL 2 Z ⇒ compactify to d = 4 on elliptically fibered CY4 with base B 6 : E τ → X 4 ↓ B ⊃ S

Gauge degrees of freedom/D-branes in F-theory F-theory: realizes (stacks of) branes in terms of geometric singularities Singularity type: y 2 = x 2 + z n + 1 A n : y 2 = x 2 z + z n − 1 D n : y 2 = x 3 + z 4 E 6 : Perturbative interpretation: A n : IIB with D7-branes D n : IIB orientifolded with D7 and O-planes E n : no perturbative IIB picture, ”exceptional 7-branes”

Matter fields [BHV I, II], [Donagi, Wijnholt] 7-branes inside B 6 wrapping surfaces, which intersect over a curve Σ : ⇒ = Bifundamental matter is localized along curves Σ ⇒ G Σ → SU (5) × U (1), in particular: SU (6) : 5 , ¯ ⇒ SO (10) : 10 , 10 5 , ⇒ Chiral matter from additional gauge fluxes

Example: SU (6) enhancement Simplest case: Switching on a single deformation on A 5 singularity y 2 = x 2 + z 6 y 2 = x 2 + ( z − λ ) z 5 → corresponds to breaking SU (6) → SU (5) × U (1). From the point of view of local enhancements: G 1 = SU (5), G 2 = U (1): → SU (5) × U (1) G Σ = SU (6) → 24 0 ⊕ 1 0 ⊕ 5 6 ⊕ 5 − 6 35 Adjoints Bifundamentals 5 ⊕ 5 are the bifundamental matter fields localized at Σ .

Yukawa couplings from Triple-Intersections [BHV I, II], [Donagi, Wijnholt] Yukawa couplings from triple intersection of matter curves: G p → SU (5) × U (1) 1 × U (1) 2 Such as SO (12) : ¯ 5 H × ¯ SU (7) : 5 × ¯ 5 M × 10 M E 6 : 10 M × 10 M × 5 H 5 × 1

SU (5) F-theory GUT [BHV II] SU(5) E6 SO(12) SO(10) SU(6) H 5 Φ i 5 Φ j ij H 5 Φ i 10 Φ j ij ¯ ⇒ W ∼ λ b 10 + λ t 10 ⇒ QDH d + LEH d + QUH u

GUT breaking [BHV I, II], [Donagi, Wijnholt] GUT-breaking by hypercharge flux F Y : SU (5) → SU (3) × SU (2) × U (1) Y 24 → ( 8 , 1 ) 0 ⊕ ( 1 , 3 ) 0 ⊕ ( 1 , 1 ) 0 ⊕ ( 3 , 2 ) − 5 ⊕ ( 3 , 2 ) + 5 Gauge Fields Exotics F Y lifts XY and solves doublet-triplet splitting: F Y | Σ M = 0 , F Y | Σ 5 H = + 1 , F Y | Σ 5 H = − 1 Masslessness of U (1) Y : imposes topological condition Ω 3 [Buican, Malyshev, Morrison, Verlinde, Wijnholt] e 1 e 2 S GUT ⇒ F Y is dual in S GUT to 2-cycle, that is homologically trivial in B

Summary of Step 1: Local model ⇒ Geometric engineering of SU (5) GUT ⇒ GUT breaking using hypercharge flux F Y ⇒ ”anything goes”, realistic SU (5) GUTs, SUSY breaking, etc. [Marsano, Saulina, SSN], [Heckman, Vafa] ⇒ Absence of dim 5 proton decay and µ -term: additional U (1)s q PQ ( H u ) + q PQ ( H d ) � = 0 U (1) PQ : ¯ ¯ 10 M 5 M 5 H 5 H For instance: − 1 − 1 U (1) PQ 2 2 ⇒ Absence of tree-level: W dim5 ∼ 1 Λ Q 3 L W ∼ µ H u H d and Summary: Local models allow lots of model building freedom

2. Constraints: Anomaly cancellation All phenomenologically viable local F-theory GUTs have additional U (1)’s (protection from proton decay, µ -term). Sources of additional constraints: • Cancellation of mixed MSSM and U (1) anomalies • Embedding into (local) CY4 geometry GUT-breaking by hypercharge ⇒ U (1) Y masslessness ensured by topological condition on F Y ⇒ F Y cannot introduce any additional gauge anomalies However: ⇒ F Y restriction on Σ 10 and Σ ¯ 5 generates chiral spectrum ⇒ Require G 2 MSSM × U (1) mixed anomaly cancellation for additional U (1)

Dudas-Palti Relations G 2 MSSM × U (1) mixed anomaly cancellation for additional U (1) imply [Dudas, Palti][Marsano][Dolan, Marsano, Saulina, SSN] ∑ Z ∑ Z q i F Y = q a F Y Σ ( i ) Σ ( a ) 10 matter curves, Σ i 5 matter curves, Σ a 10 5 10 5 Consequences of these Dudas-Palti relations: • Minimal SU (5) GUT ⇒ the only U (1) compatible is U (1) χ ( B − L and Y ) • If there is a U (1) PQ ⇒ there are always non-GUT exotics

Consequence 1: Uniqueness of U (1) χ Question: minimal SU (5) GUT with U (1). What U (1)s are possible? GUT breaking and absence of exotics requires that F Y restricts as: Z Z Z F Y = + 1 , F Y = − 1 , other Σ ′ F Y = 0 Σ Hu Σ Hd DP relations/anomaly cancellation ∑ Z ∑ Z q i F Y = q a F Y Σ ( i ) Σ ( a ) 5 matter curves, Σ a 10 matter curves, Σ i 10 5 10 5 ⇒ q H u + q H d = 0 The only possible U (1) compatible with MSSM interactions and SU (5) [Marsano, Saulina, SSN] ¯ ¯ 10 M 5 M 5 H 5 H − 1 − 2 U (1) χ 3 2 But U (1) χ does not forbid W dim 5 !