Soft SUSY breaking in Type IIA flux compactifications Dagoberto Escobar Instituto de F´ ısica Te´ orica UAM-CSIC V PostGraduate Meeting on Theoretical Physics Oviedo, November 2016 Work in progress with W. Staessens & F. Marchesano
Outline Motivation 1 Type IIA compactifications 2 Model building 3 T 6 / Z 2 × Z 2 orbifold 4 Soft SUSY breaking terms 5 Conclusions 6 Dagoberto Escobar (IFT) Soft SUSY breaking 2 / 26
Motivation SUSY is nice framework for physics beyond the Standard Model (to be experimentally confirmed at LHC) Solve the hierarchy problem Unification of gauge couplings Provide some candidates to Dark Matter If exist, SUSY must be broken on the accesible energy scale Q † Q α | 0 > � = 0 α | 0 > � = 0 Spontaneous SUSY breaking Explicit SUSY breaking Dagoberto Escobar (IFT) Soft SUSY breaking 3 / 26
Motivation SUSY is nice framework for physics beyond the Standard Model (to be experimentally confirmed at LHC) Solve the hierarchy problem Unification of gauge couplings Provide some candidates to Dark Matter If exist, SUSY must be broken on the accesible energy scale Q † Q α | 0 > � = 0 α | 0 > � = 0 Spontaneous SUSY breaking Explicit SUSY breaking We want to do this without introducing quadratic divergences. Dagoberto Escobar (IFT) Soft SUSY breaking 3 / 26
Motivation SUSY is nice framework for physics beyond the Standard Model (to be experimentally confirmed at LHC) Solve the hierarchy problem Unification of gauge couplings Provide some candidates to Dark Matter If exist, SUSY must be broken on the accesible energy scale Q † Q α | 0 > � = 0 α | 0 > � = 0 Spontaneous SUSY breaking Explicit SUSY breaking We want to do this without introducing quadratic divergences. L soft = M a λ a λ a + m 2 ij φ i ¯ j + B ij φ i φ j + A ijk φ i φ j φ k ¯ φ Dagoberto Escobar (IFT) Soft SUSY breaking 3 / 26
Motivation SUSY is nice framework for physics beyond the Standard Model (to be experimentally confirmed at LHC) Solve the hierarchy problem Unification of gauge couplings Provide some candidates to Dark Matter If exist, SUSY must be broken on the accesible energy scale Q † Q α | 0 > � = 0 α | 0 > � = 0 Spontaneous SUSY breaking Explicit SUSY breaking We want to do this without introducing quadratic divergences. L soft = M a λ a λ a + m 2 ij φ i ¯ j + B ij φ i φ j + A ijk φ i φ j φ k ¯ φ This is called soft SUSY breaking Dagoberto Escobar (IFT) Soft SUSY breaking 3 / 26
SUSY breaking basics It is difficult to directly couple a dynamical SUSY breaking to the visible sector. F-term SUSY breaking � F C α � � = 0 Require C α to be a SM singlet Does not lead to a phenomenologically viable of pattern of supersymmetry-breaking parameters. Gauginos masses cannot arise in renormalizable SUSY theory at tree-level. D-term SUSY breaking � D a � � = 0 Does not lead to a acceptable spectrum of sparticles. Soft SUSY-breaking terms should arise indirectly or radiatively, not from tree-level couplings to the SUSY breaking sector. Dagoberto Escobar (IFT) Soft SUSY breaking 4 / 26
Hidden sector framework Particles with no direct (or tiny) coupling to visible sector (i.e moduli sector in String Theory). SUSY is spontaneously broken in the hidden sector by � F h i � � = 0 Λ SUSY = � F � 1 / 2 Both sectors share some mediating interactions that transmit supersymmetry breaking from the hidden sector to the visible sector (i.e gravity ) Fields in the visible sector feel SUSY breaking at the scale m soft = Λ 2 SUSY M p Λ SUSY ∼ 10 10 − 11 GeV If we expect m soft ∼ O ( TeV ) ⇒ Dagoberto Escobar (IFT) Soft SUSY breaking 5 / 26
SUGRA effective field theory Expanding K and W in powers of the matter fields Soni & Weldon ‘83 Brignole, Iba˜ nez & Mu˜ noz ‘93 , Kaplunovsky & Louis ‘93 W ( h i ) + a α ( h i ) C α + 1 2 µ αβ ( h i ) C α C β + 1 6 Y αβγ ( h i ) C α C β C γ + .... W = ˆ � 1 � ¯ ¯ β + ¯ i ) C α C β + h . c ¯ K = ˆ K ( h i , ¯ i ) + ˜ β ( h i , ¯ i ) C α C 2 Z αβ ( h i , ¯ h K α ¯ h h + .... Expanding the SUGRA scalar potential � 1 6 A αβγ C α C β C γ + 1 � β + 2 B αβ C α C β + h . c ¯ β C α C V soft = m α ¯ The soft SUSY breaking terms are � � m � � m 2 m 2 ˜ ∂ m ∂ n ˜ K αβ − ∂ m ˜ K αγ ˜ K γδ ∂ n ˜ F n αβ = 3 / 2 + V 0 K αβ − F K δβ Dagoberto Escobar (IFT) Soft SUSY breaking 6 / 26
SUGRA effective field theory ˆ W ∗ K / 2 F m � ˆ ˆ A αβγ = e K m Y αβγ + ∂ m Y αβγ | ˆ W | � �� K δρ ∂ m ˜ ˜ − K ρα Y δβγ + ( α ↔ β ) + ( α ↔ γ ) ˆ W ∗ K / 2 � ˆ F m � � �� ˆ ˜ ρ ∂ m ˜ K δ ¯ K m µ αβ + ∂ m µ αβ − ρα µ δβ + ( α ↔ β ) B αβ = e K ¯ | ˆ W | + m 3 / 2 F m � � �� ˜ ρ ∂ m ˜ K δ ¯ � − m 3 / 2 µ αβ ∂ m Z αβ − K ¯ ρα Z δβ + ( α ↔ β ) +(2 m 2 3 / 2 + V 0 ) Z αβ − m 3 / 2 F ¯ m ∂ ¯ m Z αβ m F n � � �� ˜ ρ ∂ n ˜ − F ¯ K δ ¯ ∂ n ∂ ¯ m Z αβ − K ¯ ρα ∂ ¯ m Z δβ + ( α ↔ β ) The tree-level cosmological contant K � m − 3 m 2 � F n = κ 2 K / 2 ˆ 4 e κ 2 4 ˆ 4 e κ 2 4 ˆ V 0 = κ 2 ˆ m F n F ¯ K n ¯ m ˆ m D ¯ , W ∗ K n ¯ 3 / 2 Dagoberto Escobar (IFT) Soft SUSY breaking 7 / 26
Any prediction of soft-SUSY breaking parameters require Dagoberto Escobar (IFT) Soft SUSY breaking 8 / 26
Any prediction of soft-SUSY breaking parameters require Knowledge of the K¨ ahler metric for matter fields (normalization of the matter fields). Dagoberto Escobar (IFT) Soft SUSY breaking 8 / 26
Any prediction of soft-SUSY breaking parameters require Knowledge of the K¨ ahler metric for matter fields (normalization of the matter fields). Determine the underlying source of SUSY breaking ( related to moduli stabilisation ). Soft SUSY breaking terms from string compactifications Heterotic compactifications Brignole, Iba˜ nez & Mu˜ noz ‘93 , Brignole, Iba˜ nez, Mu˜ noz & Scheich ‘96 , Kim & Mu˜ noz ‘96 Lack of potential to stabilise moduli Type IIB compactifications (KKLT,LVS), Camara, Iba˜ nez & Uranga ‘04 ,Conlon, Cremades & Quevedo ‘05 , Conlon, Quevedo & Suruliz ‘06 , Aparicio et al. ‘14 SUSY is broken by background fluxes (non-perturbative effects to stabilise K¨ ahler moduli) Dagoberto Escobar (IFT) Soft SUSY breaking 8 / 26
Type IIA Orientifolds Compactification of Type IIA String Theory on CY orientifolds. Discrete symmetry O = ( − 1) F L Ω p R R : J = − J e 2 i θ ¯ R : Ω = Ω N = 1 SUGRA theory in 4d (closed string sector) Grimm & Louis ‘05 Massless spectrum: h (1 , 1) ahler moduli, h (2 , 1) complex structure moduli, K¨ − axion-dilaton multiplet and h (1 , 1) vector multiplets + The K¨ ahler potential � 1 � 6 K abc ( T a + ¯ T a )( T b + ¯ T b )( T c + ¯ ˆ T c ) K = − ln � F KL N L �� N K + ¯ N L + ¯ � N K � � − 2 ln 2 If background fluxes are turning on W IIA = e 0 + ie a T a − 1 2 K abc q a T b T c − im 0 6 K abc T a T b T c − h K N K ˆ Dagoberto Escobar (IFT) Soft SUSY breaking 9 / 26
Dp-branes String Theory contains extended objects with p -spatial dimensions where the endpoints of open strings are attached Polchinski ‘95 Space-time filling Dp-branes W p +1 = M (1 , 3) × Π p − 3 Dagoberto Escobar (IFT) Soft SUSY breaking 10 / 26
Dp-branes String Theory contains extended objects with p -spatial dimensions where the endpoints of open strings are attached Polchinski ‘95 Space-time filling Dp-branes W p +1 = M (1 , 3) × Π p − 3 Properties of Dp-branes Dagoberto Escobar (IFT) Soft SUSY breaking 10 / 26
Dp-branes String Theory contains extended objects with p -spatial dimensions where the endpoints of open strings are attached Polchinski ‘95 Space-time filling Dp-branes W p +1 = M (1 , 3) × Π p − 3 Properties of Dp-branes Dagoberto Escobar (IFT) Soft SUSY breaking 10 / 26
Dp-branes String Theory contains extended objects with p -spatial dimensions where the endpoints of open strings are attached Polchinski ‘95 Space-time filling Dp-branes W p +1 = M (1 , 3) × Π p − 3 Properties of Dp-branes U (1) gauge theory for a single Dp-brane. Dagoberto Escobar (IFT) Soft SUSY breaking 10 / 26
Dp-branes String Theory contains extended objects with p -spatial dimensions where the endpoints of open strings are attached Polchinski ‘95 Space-time filling Dp-branes W p +1 = M (1 , 3) × Π p − 3 Properties of Dp-branes U (1) gauge theory for a single Dp-brane. N concident Dp-branes support U ( N ) gauge theory on their worldvolume. Gauge coupling constant g − 2 ∼ Vol (Π p − 3 ) a Dagoberto Escobar (IFT) Soft SUSY breaking 10 / 26
Dp-branes String Theory contains extended objects with p -spatial dimensions where the endpoints of open strings are attached Polchinski ‘95 Space-time filling Dp-branes W p +1 = M (1 , 3) × Π p − 3 Properties of Dp-branes U (1) gauge theory for a single Dp-brane. N concident Dp-branes support U ( N ) gauge theory on their worldvolume. Gauge coupling constant g − 2 ∼ Vol (Π p − 3 ) a Type IIA String Theory contains Dp-branes with p = 0 , 2 , 4 , 6 , 8 Dagoberto Escobar (IFT) Soft SUSY breaking 10 / 26
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