Weak Gravity Conjecture constraints on the SM and Beyond Víctor Martín Lozano Universität Bonn Bethe Center for Theoretica Physics "#anez$ M-L, Valenzue a &'()*+),-./0 234! '('' 5/)'(6 0** "#anez$ M-L, Valenzue a &'()(+),1''0 Víctor Martín Lozano % Uni Bonn SUSY /)'8 Introduction Naturalness problems: Cosmological constant EW hierarchy problem Víctor Martín Lozano % Uni Bonn SUSY /)'8 Introduction Naturalness problems: Cosmological constant EW hierarchy problem LHC Víctor Martín Lozano % Uni Bonn SUSY /)'8 Introduction Naturalness problems: Cosmological constant † EW hierarchy problem LHC † Yet, so far... Víctor Martín Lozano % Uni Bonn SUSY /)'8 Introduction Naturalness problems: Cosmological constant EW hierarchy problem LHC Numerical Coincidence: Víctor Martín Lozano % Uni Bonn SUSY /)'8 Introduction !bsence of New #hysics forces us to think di%erently about the guiding principles of HE# Maybe the U( structure is telling us ho" the IR should beha*e +uantum ,ra*ity Constraints Víctor Martín Lozano % Uni Bonn SUSY /)'8 Quantum Gravity Constraints Not e*erything is possible within -tring Theory/+uantum Gra*ity Víctor Martín Lozano % Uni Bonn SUSY /)'8 Quantum Gravity Constraints Not e*erything is possible within -tring Theory/+uantum Gra*ity Not e*ery e%ecti*e theory can be embedded in Q,: -"ampland!0 1(afa 2345 Víctor Martín Lozano % Uni Bonn SUSY /)'8 Quantum Gravity Constraints #icture by Irene (alenzuela Víctor Martín Lozano % Uni Bonn SUSY /)'8 Quantum Gravity Conjectures Guiding principles to build an e%ecti*e theory consistent with +, Common features of the string landscape, model building failures, blac$ hole arguments. -Absence of global symmetries 1:an$s8;ison 2<<5 1Horo"it6, Strominger, Seiberg. 5 -Completeness hypothesis 1#olchins$i 23=5 -Wea$ ,ra*ity Conjecture 1!r$ani8Hamed et al 2345 8-"ampland constraints about the moduli space 1>oguri8(afa 2345 .hese conjectures could ha*e a signi9cant impact on low energy physics00 Víctor Martín Lozano % Uni Bonn SUSY /)'8 Weak Gravity Conjecture 1!r$ani8Hamed et al 2345 In theories of +G with a p-form gauge field, there must be an electrically charged object with charge Q and tension T such that: In order to allo" for e?tremal blac$ holes to decay (remnants) ,ra*ity must be al"ays "ea$er than any other interaction Víctor Martín Lozano % Uni Bonn SUSY /)'8 Weak Gravity Conjecture 1!r$ani8Hamed et al 2345 In theories of +G with a p-form gauge field, there must be an electrically charged object with charge Q and tension T such that: In order to allo" for e?tremal blac$ holes to decay (remnants) ,ra*ity must be al"ays "ea$er than any other interaction -harpened version of the WGC: 1>oguri 8 (afa 2B45 Non-S'-Y AdS *acua cannot be consistent with Q, 8It also applies to lo"er dimensional *acua 8.he !dS vacua must be stable Víctor Martín Lozano % Uni Bonn SUSY /)'8 Weak Gravity Conjecture 1!r$ani8Hamed et al 2345 In theories of +G with a p-form gauge field, there must be an electrically charged object with charge Q and tension T such that: In order to allo" for e?tremal blac$ holes to decay (remnants) ,ra*ity must be al"ays "ea$er than any other interaction -harpened version of the WGC: 1>oguri 8 (afa 2B45 Non-S'-Y AdS *acua cannot be consistent with Q, -M compacti9cations should be also consistent with Q, Víctor Martín Lozano % Uni Bonn SUSY /)'8 Compactifications of the SM to 3D 1!r$ani8Hamed et al 23D5 Standard &odel + ,ravity on : 1!rnold8Eornal8Wise 2B35 Casimir Energy >ne-loop corrections: , ;epending on the light mass spectra and the c.c we could get !dS *acua00 Looking at the whole spectrum one can 9nd inconsistencies that can be sol*ed assuming -'-Y for instance 1,on6alo, Herráez, IbFGez 2B<5 Víctor Martín Lozano % Uni Bonn SUSY /)'8 Compactifications of the SM to 3D Standard &odel + ,ravity on : Víctor Martín Lozano % Uni Bonn SUSY /)'8 Compactifications of the SM to 3D Standard &odel + ,ravity on : Víctor Martín Lozano % Uni Bonn SUSY /)'8 Compactifications of the SM to 3D Standard &odel + ,ravity on : Normal Inverted Hierarchy Hierarchy @NHA @IH) Víctor Martín Lozano % Uni Bonn SUSY /)'8 Compactifications of the SM to 3D Standard &odel + ,ravity on : Majorana Neutrinos Víctor Martín Lozano % Uni Bonn SUSY /)'8 Compactifications of the SM to 3D Standard &odel + ,ravity on : ;irac Neutrinos Víctor Martín Lozano % Uni Bonn SUSY /)'8 Constraints on neutrino masses Majorana Neutrinos !dS vacuum for any *alue of )'LE; >'.0 ;irac Neutrinos NH IH No *acuum < 6.7 meV < 2.1 me( *acuum 4 7 meV < < 7.7 me( 2.1 me( H < 2.56 me( *acuum > 7.7 me( > 2.56 me( < 7.7 meV (NH) H 2.56 meV (IH) Víctor Martín Lozano % Uni Bonn SUSY /)'8 Lo"er bound on the Cosmological Constant &ajorana (DiracA Eirst argument to ha*e , not based on Cosmology Víctor Martín Lozano % Uni Bonn SUSY /)'8 'pper bound on the EW scale Majorana Neutrinos ;irac Neutrinos #arameters leading to a higher EW scale: Inconsistency with quantum gravity .here is also a lo"er bound: 1,on6alo, IbFGez 2B<5 Víctor Martín Lozano % Uni Bonn SUSY /)'8 :-& Physics : Weyl Fermion Majorana Neutrinos ;irac Neutrinos Víctor Martín Lozano % Uni Bonn SUSY /)'8 :-& Physics : Dirac Fermion Majorana Neutrinos ;irac Neutrinos Víctor Martín Lozano % Uni Bonn SUSY /)'8 :-& Physics : Axion .he presence of the a?ion ma$es the Majorana Neutrinos !dS vacuum deeper ;irac Neutrinos Víctor Martín Lozano % Uni Bonn SUSY /)'8 Conclusions Not e*ery effecti*e theory can be embedded into +, @+, conjectures) Consistency with Q, implies constraints low energy physics !dS Instability Conjecture + stability of 3D SM vacua: 8 Lo"er bound on the cosmological constant and upper bound on neutrino masses 8 Upper bound on the EW scale in terms of the c.c Víctor Martín Lozano % Uni Bonn SUSY /)'8 .