LARGE Volume Models and Superstring Cosmophysics Joseph Conlon, Oxford University 3rd UTQuest Workshop, Hokkaido, 10th August 2012 Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Plan Plan of these two lectures: 1. The LARGE volume scenario ◮ Construction ◮ Moduli spectrum ◮ Structure of susy breaking 2. Applications to cosmology Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Why String Cosmophysics? String theory is a theory of quantum gravity whose natural scale is M P ∼ 2 . 4 × 10 18 GeV. Interesting cosmological scales ◮ Inflation: V inf � (10 16 GeV) 4 ◮ . . . ◮ QCD phase transition: V ∼ (200MeV) 4 ◮ BBN: V BBN ∼ (1MeV) 4 ◮ Late-time acceleration: V Λ ∼ (10 − 3 eV) 4 All are ≪ M P . Why care about string theory? Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Why String Cosmophysics? String theory is a ten dimensional theory and we need to compactify. The geometric parameters of the extra dimensions turn into 4-dimensional scalar fields called moduli . These moduli are ubiquitous in string compactifications. ◮ Moduli are good inflaton candidates. Unstabilised, they destroy candidate inflationary models. ◮ Moduli last. They are gravitationally coupled and dominate the energy density. ◮ Moduli dynamics break supersymmetry. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Why String Cosmophysics: Inflation ′′ Inflation requires a flat potential with η ∼ M 2 P V ≪ 1 along the V inflaton direction and no runaways. Flatness of inflation requires control of Planck-suppressed operators: � � 1 + φ 2 V = V 0 + . . . M 2 P would generate O (1) correction to η . Decompactification moduli (dilaton and volume) couple to everything. Unstabilised, these decompactify inflaton potential. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Why String Cosmophysics: Moduli Lifetimes Moduli are gravitationally coupled and are long-lived: m 3 Γ ∼ 1 � m φ � − 3 φ ∼ 1sec M 2 4 π 30TeV P � m φ � 3 / 2 T reheat ∼ (1MeV) 30Tev Moduli oscillate after inflation and redshift as matter. They decay late with low reheating temperatures, and can forbid leptogenesis, thermal WIMP dark matter, electroweak baryogenesis.... Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Why String Cosmophysics? If string theory is true: ◮ You may be able to study the initial singularity without worrying about moduli ◮ You cannot study the post-inflationary universe without worrying about moduli In particular I want to emphasise that conventional moduli dynamics often render impossible many ideas such as thermal leptogenesis, electroweak baryogenesis, thermal WIMP dark matter, Big Bang Nucleosynthesis..... If our universe involves string theory, we need to study moduli. To study moduli we need to study moduli stabilisation. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Moduli Stabilisation Moduli stabilisation is about creating a potential for moduli with a stable minimum. Nature is hierarchical, and interesting moduli stabilisation scenarios generate hierarchies. I am going to focus on the LARGE volume scenario in IIB flux compactifications. By breaking supersymmetry and stabilising the volume at exponentially large values, this gives good control and attractive phenomenology. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
LARGE Volume Models Consider IIB flux compactifications. The leading order 4-dimensional supergravity theory is � � � � � Ω ∧ ¯ S + ¯ K = − 2 ln ( V ) − ln i Ω − ln S , � = G 3 ∧ Ω . W This fixes dilaton and complex structure but is no-scale with respect to the K¨ ahler moduli. No-scale models have ◮ Vanishing cosmological constant ◮ Broken supersymmetry ◮ Unfixed flat directions Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Moduli Stabilisation: Fluxes ◮ The effective supergravity theory is � � � Ω ∧ ¯ − ln( S + ¯ K = − 2 ln( V ) − ln i Ω S ) � � W = ( F 3 + iSH 3 ) ∧ Ω ≡ G 3 ∧ Ω . ◮ This stabilises the dilaton and complex structure moduli. D S W = D U W = 0 . � W = G 3 ∧ Ω = W 0 . Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Moduli Stabilisation: Fluxes The theory has an important no-scale property. � � � � � � � ˆ V ( T + ¯ Ω ∧ ¯ S + ¯ = − 2 ln T ) − ln Ω( U ) − ln K i S , � W = G 3 ∧ Ω ( S , U ) . � � ˆ K α ¯ K i ¯ K ˆ β D α WD ¯ β ¯ ˆ j D i WD ¯ j ¯ W − 3 | W | 2 = W + V e U , S T � ˆ K α ¯ ˆ β D α WD ¯ β ¯ = 0 . K = e W U , S Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Moduli Stabilisation: Fluxes � � ˆ V ( T i + ¯ K = − 2 ln T i ) , = W W 0 . �� � ˆ K i ¯ ˆ j ¯ K j D i WD ¯ W − 3 | W | 2 V = e T = 0 No-scale model : ◮ vanishing vacuum energy ◮ broken susy ◮ T unstabilised No-scale is broken perturbatively and non-pertubatively. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Moduli Stabilisation: KKLT � � � � � ˆ Ω ∧ ¯ S + ¯ = − 2 ln ( V ) − ln Ω − ln K i S , � � A i e − a i T i . W = G 3 ∧ Ω+ i Non-perturbative effects (D3-instantons / gaugino condensation) allow the T -moduli to be stabilised by solving D T W = 0. For consistency, this requires �� � W 0 = G 3 ∧ Ω ≪ 1 . Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Moduli Stabilisation: KKLT ˆ = − 2 ln ( V ) , K � A i e − a i T i . = W 0 + W i Solving D T W = ∂ T W + ( ∂ T K ) W = 0 gives Re( T ) ∼ 1 a ln( W 0 ) For Re( T ) to be large, W 0 must be enormously small. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
LARGE Volume Models Going beyond no-scale the appropriate 4-dimensional supergravity theory is � � � � � V + ξ � � Ω ∧ ¯ S + ¯ K = − 2 ln − ln i Ω − ln S , g 3 / 2 s � � A i e − a i T i . = G 3 ∧ Ω + W i Key ingredients are: (1) the inclusion of stringy α ′ corrections to the K¨ ahler potential (2) nonperturbative instanton corrections in the superpotential. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
LARGE Volume Models The simplest model (the Calabi-Yau P 4 [1 , 1 , 1 , 6 , 9] ) has two moduli and a ‘Swiss-cheese’ structure: � � τ 3 / 2 − τ 3 / 2 V = . s b Computing the moduli scalar potential, we get for V ≫ 1, √ τ s a 2 s | A s | 2 e − 2 a s τ s − a s | A s W | τ s e − a s τ s + ξ | W | 2 V = V 3 . V 2 g 3 / 2 V s The minimum of this potential can be found analytically. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Moduli Stabilisation: LARGE Volume √ τ s a 2 s | A s | 2 e − 2 a s τ s − a s | A s W 0 | τ s e − a s τ s + ξ | W 0 | 2 V = V 3 . V 2 g 3 / 2 V s � �� � Integrate out heavy mode τ s −| W 0 | 2 (ln V ) 3 / 2 + ξ | W 0 | 2 V = V 3 . V 3 g 3 / 2 s A minimum exists at τ s ∼ ξ 2 / 3 V ∼ | W 0 | e a s τ s , . g s This minimum is non-supersymmetric AdS and at exponentially large volume. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
LARGE Volume Models The locus of the minimum satisfies V ∼ | W | e c / g s , τ s ∼ ln V . The minimum is at exponentially large volume and non-supersymmetric. The large volume lowers the string scale and supersymmetry scale through m s ∼ M P m 3 / 2 ∼ M P √ , V . V An appropriate choice of volume will generate TeV scale soft terms and allow a supersymmetric solution of the hierarchy problem. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
LARGE Volume Models BULK BLOW−UP U(2) Q L e L U(3) U(1) e R Q R U(1) Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Moduli Stabilisation: LARGE Volume Question: LVS uses an α ′ correction to the effective action. If some α ′ corrections are important, won’t all will be? Truncation is self-consistent because minimum exists at exponentially large volumes. The inverse volume is the expansion parameter and so it is consistent to only include the leading α ′ corections. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Moduli Stabilisation: LARGE Volume Higher α ′ corrections are suppressed by more powers of volume. Example: � � d 10 x √ g G 2 d 10 x √ g R 4 3 R 3 : � �� � � �� � d 4 x √ g 4 d 6 x √ g 6 G 2 d 4 x √ g 4 d 6 x √ g 6 R 4 3 R 3 : � � d 4 x √ g 4 d 4 x √ g 4 � V × V − 4 / 3 � V × V − 1 × V − 1 � � : � � d 4 x √ g 4 d 4 x √ g 4 � V − 1 / 3 � � V − 1 � : Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Recommend
More recommend
