Weak gravity conjecture, Multiple point principle and SM landscape - PowerPoint PPT Presentation

Weak gravity conjecture, Multiple point principle and SM landscape Yuta Hamada (UW-Madison&KEK→APC Paris&Crete) w/ Gary Shiu(UW-Madison) JHEP1711(2017)043 02/14/2018 KEK-PH 2018

People used to think decoupled. independent from gravity (SM, beyond SM). • If (Energy) ≪ M P , effect of gravity is • Model building below Planck scale is

People used to think model building. • This might not true . • Gravity may say something about low energy [Vafa ‘05]

Motivation by SM physics. Gravity is weakest force. 
 All non-SUSY AdS vacua are unstable. The parameters of the theory are tuned so that 
 many vacua are degenerate in energy. • Test conjectures about quantum gravity 
 • Conjecture1: Weak Gravity Conjecture 
 • Conjecture2: Multiple Point criticality Principle 


Talk Plan 1. Conjectures 2. Standard Model on M 4 3. Standard Model on M 3 × S 1

Talk Plan 1. Conjectures 2. Standard Model on M 4 3. Standard Model on M 3 × S 1

Weak gravity conjecture(WGC) Gravity is weakest force. WGC requires 
 (gauge force) ≧ (gravity force) 
 q, m q ≧ m/M P [Arkani-Hamed, Motl, Nicolis, Vafa ‘06] • Conjecture: 
 • q: gauge charge. 


Non-SUSY AdS conjecture Except for BPS state, gravity is strictly weakest force. 
 
 All non-SUSY AdS vacua supported by flux are unstable. Motivation: It is unnatural that non-BPS state saturates WGC under quantum correction . Motivation: (All known construction from M/string theory, 
 AdS is supported by some flux.) + (Conjecture1) Implication of conjecture1. [Ooguri, Vafa ‘16] • Conjecture1: 
 • Conjecture2: All non-SUSY AdS vacua are unstable.

Multiple point principle(MPP) The parameters of the theory are tuned so that many vacua are degenerate in energy. from vast landscape. [Froggatt, Nielsen ’95][Bennett ‘96] • Conjecture: 
 • Possible principle to extract predictions 


？ Motivation of MPP QFT Statical mechanics micro-canonical Equivalent in thermodynamic limit canonical In statical mechanics, micro-canonical ensemble is fundamental. 
 First, E(extensive variable) is given, and T(intensive variable) appears as a result.

Motivation of MPP QFT Statical mechanics micro-canonical Proposal in [Froggatt, Nielsen ’95] Equivalent in thermodynamic limit canonical Correspondence: 
 T ↔ coupling(intensive variable), 
 E ↔∫ φ 2 (extensive variable).

Coexisting phase tuned to be boiling point T * . • Add heat to water under constant pressure. • Point: For wide range of E, the temperature T is

QFT version is realized as an average between two vacuum. vacua should be degenerate. • Inspired by micro-canonical ensemble, we fix I 2. • Taking natural value I 2 =O(V 4 M P2 ), the constraint • To maintain coexisting phase, 


Talk Plan 1. Conjectures 2. Standard Model on M 4 3. Standard Model on M 3 × S 1

AdS vacuum in SM can have AdS 4 minimum, 
 depending on 
 M t , M H 
 and higher dim. operator • 4d SM Higgs potential 
 [Degrassi et. al. ’12, …]

SM Higgs potential Application of WGC Depending on M t , M H and higher-dim operators, high scale AdS vacuum appears. WGC can constrain top & Higgs mass. [YH, Shiu ‘17] Application of MPP Requiring the degenerate vacua, the predictions on M H , M t are obtained. The correct M H was predicted 20 years ago. [Froggatt, Nielsen ’95]

Talk Plan 1. Conjectures 2. Standard Model on M 4 3. Standard Model on M 3 × S 1

S 1 compactification of SM [Arkani-Hamed, Dubovsky, Nicolis, Villadoro ‘07] potential for radion L One-loop effective potential (Casimir energy)

S 1 compactification of SM vacuum around neutrino mass scale [Arkani-Hamed, Dubovsky, Nicolis, Villadoro ‘07] potential for radion L [YH, Shiu ‘17] bc & mass of ν [See also Ooguri Vafa ’16, Ibanez et. al. ‘17]

Application of WGC decay non-perturbatively. [YH, Shiu ‘17] • Neutrino vacuum can be AdS, but it is likely to • Consistent with the conjecture. Runaway behavior for small radius

Application of MPP between 3D and 4D vacua. Predicted neutrino mass is 
 m ν,lightest =O(1-10)meV, and neutrino is Dirac. [YH, Shiu ‘17] • We may consider the degeneracy 
 V • 
 4D 3D L

Summary Related to Stability of the electroweak vacuum. Prediction: 
 Neutrino is Dirac, and m ν,lightest = O(1-10)meV. • Conjecture1: Weak Gravity Conjecture 
 • Conjecture2: Multiple Point criticality Principle 


Backup

Quantum gravity & SM physics by SM physics. Gravity is weakest force. 
 Non-SUSY AdS vacua are unstable.(sharpened ver.) The parameters of the theory are tuned so that 
 many vacua are degenerate in energy. • Motivation: Test of conjectures about quantum gravity 
 • Conjecture1: Weak Gravity Conjecture 
 [Arkani-Hamed, Motl, Nicolis, Vafa ‘06] [Ooguri, Vafa ‘16] • Conjecture2: Multiple Point criticality Principle 
 [Froggatt, Nielsen ’95]

Test1: Higgs potentials [Degrassi et. al. ’12, …] central value M t =173GeV & c 6 =0, smaller M t ⪅ 171GeV, EW vacuum is metastable. EW vacuum is absolutely stable. 1. × 10 70 c 6 = 1 5. × 10 69 c 6 = 0 V [ GeV 4 ] c 6 =- 1 0 - 5. × 10 69 M t = 173GeV - 1. × 10 70 5. × 10 17 1.5 × 10 18 2.5 × 10 18 0 h [ GeV ] λ <0 for h > 10 10 GeV . Requiring the degenerate vacua, the predictions on M H , M t are obtained. The correct M H was predicted 20 years ago. [Froggatt, Nielsen ’95]

Test2: S 1 compactification of SM d.o.f. γ+graviton: 4 ν: 2×3=6 cc dominates ν dominates Λ4(positive) γ+graviton(negative) ν(negative/positive z=0or1) balance among [Arkani-Hamed, Dubovsky, Nicolis, Villadoro ‘07] potential for radion L bc & mass of ν

Summary place to test various conjectures. Neutrino is Dirac, and m ν,lightest = O(1-10)meV. • SM Higgs potential and SM landscape are good • Multiple Point criticality Principle predicts 


AdS vacuum in SM on S 1 There is AdS 3 minimum. • potential for radion field. 
 bc & mass of ν