Lisa Randall, Harvard University AA NewNew ViewView ofof WeakWeak ScaleScale PhysicsPhysics ManyMany newnew resultsresults inin theoreticaltheoretical physicsphysics SomeSome ofof thethe mostmost excitingexciting involveinvolve extraextra dimensionsdimensions ofof spacespace IntriguingIntriguing possibilitiespossibilities forfor ourour universe:universe: bothboth theoreticaltheoretical andand experimentalexperimental WarpedWarped geometrygeometry hashas particularlyparticularly interestinginteresting signatures:signatures: resonances!resonances! ExtraExtra dimensionsdimensions ofof spacespace couldcould bebe thethe nextnext bigbig discoverydiscovery atat CERNCERN SamplingSampling ofof whatwhat wewe nownow knowknow isis possiblepossible——inin physics!physics!

BraneworldsBraneworlds andand MultiversesMultiverses ExtraExtra dimensionsdimensions cancan bebe infinitelyinfinitely large,large, yetyet bebe invisibleinvisible NewNew placeplace inin thethe universe:universe: threethree--dimensionaldimensional sinkholesinkhole ExtraExtra dimensionsdimensions cancan illuminateilluminate connections,connections, resolvingresolving puzzlespuzzles ofof aa 3+13+1 dimensionaldimensional worldworld WithWith testabletestable experimentalexperimental consequencesconsequences WhyWhy shouldshould suchsuch differentdifferent resultsresults connect?connect? HighHigh--energyenergy physicsphysics coverscovers anan enormousenormous rangerange ofof energiesenergies AtAt thethe highesthighest energies,energies, wewe needneed aa theorytheory ofof quantumquantum gravitygravity——aa theorytheory thatthat includesincludes quantumquantum mechanicsmechanics andand generalgeneral relativityrelativity StringString theory,theory, inin whichwhich thethe fundamentalfundamental ingredientsingredients areare oscillating,oscillating, vibratingvibrating strings,strings, isis thethe leadingleading candidatecandidate LowerLower Energies?Energies?

AtAt lowerlower energyenergy scales,scales, therethere areare physicalphysical phenomenaphenomena thatthat wewe cancan studystudy experimentallyexperimentally UnderstandUnderstand basicbasic elementselements ofof mattermatter andand theirtheir interactionsinteractions NewNew ideasideas mightmight provideprovide deeperdeeper connectionsconnections amongamong knownknown physicalphysical quantities:quantities: masses,masses, forcesforces TheseThese areare theoriestheories wewe cancan experimentallyexperimentally testtest TheThe bestbest route?route?

Model Building: adventure travel through world of ideas ExtraExtra DimensionsDimensions OneOne Route?Route?

StringString theory:theory: extraextra dimensionsdimensions essentialessential LowerLower energies:energies: ExtraExtra dimensionsdimensions cancan illuminateilluminate connectionsconnections amongamong observableobservable phenomenaphenomena inin newnew waysways TheyThey areare afterafter allall aa possibilitypossibility fromfrom perspectiveperspective ofof generalgeneral relativityrelativity Plus:Plus: Bonus:Bonus: EvenEven shedshed lightlight onon purelypurely fourfour-- dimensionaldimensional physicsphysics ExtraExtra DimensionsDimensions inin PhysicsPhysics

TheodorTheodor KaluzaKaluza proposedproposed extraextra dimensionsdimensions inin 19191919 EinsteinEinstein (referee)(referee) delayeddelayed publicationpublication forfor twotwo yearsyears InterestingInteresting idea,idea, butbut whatwhat makesmakes thethe otherother dimensiondimension different?different? OldOld answeranswer:: ExtraExtra dimensionsdimensions cancan bebe rolledrolled upup toto aa tinytiny sizesize ™™ButBut AlsoAlso NewNew AnswersAnswers…… HoseHose AcrossAcross FootballFootball FieldField Oskar Klein proposed idea that dimension is rolled up in 1926 If a dimension is wound sufficiently tightly you won’t see it

1 Dimensional

Can see 2D or 3D with small probe

Very intuitive; if sufficiently tiny, it doesn’t look like it’s there CurledCurled--upup DimensionDimension

Entire universe is curled up! NewNew (1999)(1999) WayWay toto HideHide DimensionsDimensions BasedBased onon anan importantimportant ingredientingredient inin ““stringstring”” theorytheory whosewhose importanceimportance waswas onlyonly recentlyrecently recognizedrecognized BRANESBRANES MembraneMembrane--likelike objectsobjects inin higherhigher dimensionaldimensional spacespace PlayPlay anan essentialessential rolerole inin stringstring theorytheory WhatWhat’’ss New?New? BranesBranes

Branes:Branes: DistinguishDistinguish dimensionsdimensions alongalong aa branebrane fromfrom thosethose perpendicularperpendicular toto itit BranesBranes cancan traptrap particlesparticles andand forcesforces

Stuck on a brane like a bead on a wire

Particles stuck on a brane like beads on a wire DD--Branes:Branes: WhereWhere OpenOpen StringsStrings EndEnd

Particles and forces stuck on branes—not gravity! WhyWhy notnot gravity?gravity?

GravityGravity ------closedclosed string:string: nono ends!ends!

Energy:Energy: allall energyenergy interactsinteracts viavia gravitygravity

Geometry:Geometry: gravitygravity connectedconnected toto spacetimespacetime BraneworldBraneworld HigherHigher--dimensionaldimensional worldworld inin whichwhich particlesparticles andand mattermatter areare stuckstuck onon aa branebrane

Drawn as 2D Really 3D And really infinite

WithWith branes,branes, wewe’’veve foundfound warpedwarped geometrygeometry SolutionsSolutions thatthat provide:provide: NewNew wayway toto hidehide dimensionsdimensions NewNew wayway toto explainexplain weaknessweakness ofof gravitygravity NewNew conceptconcept ofof ourour placeplace inin thethe universeuniverse RS2RS2 BraneworldBraneworld—— NewNew wayway toto hidehide aa dimensiondimension (LR with Raman Sundrum)

Extra dimension can be infinite in size! Spacetime is warped and gravity stays near the brane. LocalizedLocalized Gravity:Gravity: WarpedWarped GeometryGeometry

We solved equations for gravity and according to Einstein’s General Relativity All of spacetime is warped

GravityGravity isis concentratedconcentrated nearnear thethe branebrane

Tiny probability for gravity to leak away from brane GravitationalGravitational FieldField NearNear BraneBrane

Force spreads very asymmetrically Lines of gravitational force almost parallel to brane Gravity doesn’t leak into extra dimension as you would expect without warping Localized gravity: new way to hide dimensions ExtraExtra dimensiondimension cancan bebe infiniteinfinite inin sizesize WithoutWithout usus knowingknowing aboutabout itit BecauseBecause warpedwarped gravitygravity spreadsspreads outout inin onlyonly threethree spatialspatial dimensionsdimensions ------NotNot fourfour (really,(really, tinytiny amountamount inin fourth)fourth)

AlternativeAlternative toto rolledrolled--upup dimension!dimension! EvenEven MoreMore Dramatic:Dramatic: LocalityLocality ofof FourFour DimensionsDimensions WhyWhy shouldshould youyou needneed toto knowknow aboutabout spacespace farfar fromfrom thethe branebrane?? WithWith AndreasAndreas KarchKarch,, foundfound fourfour--dimensionaldimensional gravitygravity nearnear thethe branebrane ButBut higherhigher--dd everywhereeverywhere elseelse FourFour--dimensionaldimensional sinkholesinkhole ExcitingExciting butbut frustratingfrustrating

CouldCould existexist somethingsomething asas dramaticdramatic asas anan infiniteinfinite extraextra dimension,dimension, pocketspockets ofof lowerlower-- dimensionaldimensional space,space, butbut wewe wouldnwouldn’’tt knowknow it!it! CanCan aa warpedwarped extraextra dimensiondimension bebe testedtested?? Yes,Yes, ifif connectedconnected toto ParticleParticle PhysicsPhysics HierarchyHierarchy Problem:Problem: OneOne ofof thethe biggestbiggest puzzlespuzzles inin particleparticle physicsphysics WhyWhy isis gravitygravity soso weakweak comparedcompared toto thethe otherother elementaryelementary forces?forces?

MightMight notnot seemseem weakweak butbut magnetmagnet cancan taketake onon thethe entireentire Earth-Earth- HierarchyHierarchy ProblemProblem

Need “fine-tuning” to get very different masses Key issue in particle physics today One that will be resolved at LHC ““FineFine--tuningtuning”” isis unlikely:unlikely: NoNo artistartist soso wewe needneed anan explanationexplanation

Barnett Newman: Broken Obelisk RS1RS1 ““MultiverseMultiverse::”” WarpedWarped SpacetimeSpacetime GeometryGeometry LikeLike BeforeBefore

•Now two branes •Gravity still concentrated on Gravitybrane •But we live on a second brane: •The Weakbrane NaturalNatural forfor gravitygravity toto bebe weak!weak!

IfIf wewe livelive anywhereanywhere butbut thethe GravitybraneGravitybrane,, gravitygravity willwill seemseem weakweak SmallSmall probabilityprobability forfor gravitongraviton toto bebe nearnear thethe WeakbraneWeakbrane NaturalNatural consequenceconsequence ofof warpedwarped geometrygeometry RescalingRescaling AcrossAcross FifthFifth DimensionDimension EverythingEverything rescaledrescaled inin warpedwarped geometry!geometry!

Can understand weakness of gravity as things being bigger and lighter on the Weakbrane WhatWhat rescalingrescaling meansmeans::

AnythingAnything onon oror nearnear thethe WeakbraneWeakbrane hashas OrderOrder TeVTeV--scalescale massmass AnythingAnything localizedlocalized inin thethe bulkbulk hashas CorrespondinglyCorrespondingly exponentiallyexponentially biggerbigger massmass OnOn GravitybraneGravitybrane--backback toto PlanckPlanck--scalescale massesmasses ParticlesParticles inin bulkbulk

Planck 106 TeV 1000 TeV TeV ExperimentalExperimental Tests?Tests?

ConnectionConnection toto massmass andand weaknessweakness ofof gravitygravity relativerelative toto otherother knownknown forcesforces tellstells usus LHCLHC willwill havehave thethe rightright energyenergy toto searchsearch forfor consequencesconsequences ofof thisthis theorytheory AnythingAnything onon thethe WeakbraneWeakbrane shouldshould havehave roughlyroughly TeVTeV energy/massenergy/mass ManyMany modesmodes onon thethe TeV/WeakbraneTeV/Weakbrane KKKK Particles:Particles: WeakWeak ScaleScale FingerprintsFingerprints ofof ExtraExtra DimensionsDimensions

WithWith extraextra dimensions,dimensions, therethere areare newnew KaluzaKaluza--KleinKlein (KK)(KK) particlesparticles TravelTravel andand carrycarry momentummomentum inin extraextra dimensionsdimensions LookLook toto usus likelike particlesparticles withwith massmass characteristiccharacteristic ofof thethe extraextra--dimensionaldimensional geometrygeometry KKKK modesmodes ofof gravitongraviton

InIn RS1,RS1, KKKK spectrumspectrum veryvery distinctivedistinctive TeVTeV,, 22 TeVTeV,, 33 TEVTEV (rough)(rough) spectrumspectrum WithWith muchmuch strongerstronger thanthan gravitationalgravitational interactioninteraction strength!strength! InteractionInteraction strengthstrength isis warpedwarped too!too!

NotNot 1/M1/MP Instead,Instead, 1/TeV1/TeV ImplicationsImplications

IfIf youyou produceproduce aa KKKK modemode ofof thethe gravitiongravition NotNot justjust missingmissing energy!energy! ModeMode decaysdecays insideinside detectordetector——justjust likelike mostmost otherother heavyheavy particlesparticles wewe hopehope toto discoverdiscover 99 MeansMeans wewe cancan reconstructreconstruct mass,mass, spinspin (we(we hope!)hope!) 99 WouldWould bebe firstfirst genuinegenuine signaturesignature ofof quantumquantum gravitygravity 99 GravitonGraviton itselfitself tootoo weaklyweakly interactinginteracting toto detectdetect directlydirectly 99 NotNot truetrue forfor itsits KKKK modes!modes! ExperimentalExperimental Signal:Signal: CanCan searchsearch forfor extraextra dimensions!dimensions!

KaluzaKaluza--KleinKlein particlesparticles DefiniteDefinite massmass spectrumspectrum andand ““spinspin””--22

¾ Truly different than other strongly interacting theories

¾ Light spin-2 but gap

¾ No other strongly interacting states as light collider signals would be dramatically different

H. Davoudiasl, J. Hewett, T. Rizzo gravitongraviton hashas spinspin 22

M=1.5 TeV 100fb-1

Angular distributions IfIf RS1RS1 solvessolves thethe hierarchyhierarchy problem,problem, wewe shouldshould bebe ableable toto telltell AndAnd ifif wewe areare veryvery lucky,lucky, fivefive--dimensionaldimensional blackblack holesholes andand stringstring statesstates mightmight alsoalso appearappear

LESSONLESSON 1:1: RS1RS1 givesgives cleanclean TeVTeV--KKKK--gravitongraviton SpinSpin--22 andand GapGap inin spectrumspectrum definitedefinite indicationindication ofof warpedwarped extraextra--dimensionaldimensional geometrygeometry LotsLots ofof stronglystrongly interactinginteracting TeVTeV--scalescale physicsphysics toto complementcomplement thisthis measurementmeasurement OtherOther warpedwarped scenariosscenarios addressingaddressing thethe hierarchy?hierarchy? RS1RS1 isnisn’’tt thethe onlyonly scenario:scenario: variationsvariations interestinginteresting DependsDepends onon whetherwhether particlesparticles onon branebrane oror inin bulkbulk TwoTwo keykey featuresfeatures thatthat makemake bulkbulk mattermatter possiblepossible ¾ Size of fifth dimension extremely small (only about 30 times fundamental scale—exponential hierarchy) ™Means you can have gauge bosons in the bulk ™Coupling won’t be too weak ¾ You only need Higgs on the Weakbrane to address the hierarchy ™Problem only for the Higgs scalar: gauge boson and fermion masses are protected SuggestsSuggests newnew scenariosscenarios

FermionsFermions and/orand/or gaugegauge bosonsbosons cancan bebe inin thethe bulkbulk BecauseBecause 5D5D cutcut--offoff isis PlanckPlanck scalescale 99AllowsAllows forfor unification!unification! AllowsAllows forfor interestinginteresting modelmodel--building:building: 99FermionFermion massesmasses fromfrom wavefunctionwavefunction overlapoverlap withwith HiggsHiggs fieldfield (on(on WeakbraneWeakbrane)) BulkBulk scenariosscenarios havehave distinctivedistinctive signaturessignatures ParticlesParticles inin bulkbulk

Planck 106 TeV 1000 TeV TeV BulkBulk UnificationUnification NetNet contributioncontribution fromfrom allall modesmodes GivesGives logarithmiclogarithmic runningrunning FromFrom TeVTeV scalescale toto PlanckPlanck scalescale LESSONLESSON 2:2: veryvery naturalnatural toto havehave unificationunification

GravityGravityGravity CouplingCouplingCoupling energyenergyenergy strengthstrengthstrength energyenergyenergy Phenomenology?Phenomenology?

BulkBulk gaugegauge bosonsbosons MeansMeans KKKK modesmodes ofof weakweak bosons,bosons, gluonsgluons asas wellwell asas gravitonsgravitons ResonancesResonances withwith strongstrong forceforce interactionsinteractions forfor exampleexample CanCan findfind gluongluon KKKK modesmodes andand distinguishdistinguish numbernumber ofof dimensionsdimensions

LESSON 2: Resonances have more Info than we’ve explored yet LR with Ben Lillie, Liantao Wangh PrecisePrecise signaturessignatures dependdepend onon fermionfermion wavefunctionwavefunction profilesprofiles MightMight expectexpect nontrivialnontrivial profilesprofiles MassesMasses dependdepend onon overlapoverlap withwith HiggsHiggs ExpectExpect lightlight fermionsfermions localizedlocalized nearnear Planck/GravityPlanck/Gravity branebrane Top,Top, bottombottom nearnear WeakbraneWeakbrane FermionFermion ProfilesProfiles andand MassesMasses DualDual InterpretationInterpretation ofof WarpedWarped ScenariosScenarios RS phenomenology has dual 4d strongly interacting conformal field theory interpretation Roughly, between Planck scale and TeV scale, CFT At TeV scale, CFT spontaneously broken Gives rise to composite states Which states are composite depends on details of wavefunction Those localized near TeV/Weak brane are more composite Those localized near Planck/Gravity brane are less composite SignaturesSignatures ofof PartialPartial CompositenessCompositeness Higgs (longitudinal modes) couplings to electroweak gauge bosons are enhanced

Long W, tR->bL KK resonances Enhanced KK production through tR loops (Agashe, Delgado, May, Sundrum) Also graviton KK resonance has interactions very similar to that of Higgs! (LR and RS) LESSON 3: RICH PHENOMENOLOGY-NOT YET FULLY EXPLORED SignaturesSignatures ofof ExtraExtra DimensionsDimensions Still?Still? StillStill havehave distinctivedistinctive spinspin--22 resonanceresonance WhatWhat otherother distinguishingdistinguishing featuresfeatures inin interactions?interactions? IsIs itit extraextra dimensionsdimensions oror justjust somesome strongstrong interactions?interactions? γγγγ,, gluongluon gluongluon interactionsinteractions shouldshould bebe thethe samesame (LR(LR withwith RS)RS) AfterAfter all,all, itit’’ss aa gravitationalgravitational interactioninteraction WorthWorth investigatinginvestigating OneOne moremore variant:variant: KRKR ModelModel

CanCan havehave RSRS withoutwithout thethe 22nd branebrane boundingbounding spacetimespacetime ThenThen getget aa gaplessgapless continuumcontinuum ofof KKKK modesmodes RatherRather thanthan resonanceresonance signatures,signatures, RevertsReverts toto missingmissing energyenergy CrossCross SectionSection andand MissingMissing EnergyEnergy

Spiropolu KR: equivalent Missing energy to n=6 searches might find KR geometry

Only distinguished by black holes and strings!

LESSON 4: Even missing energy searches can find warped scenario SummarySummary

BestBest signature:signature: spinspin--22 resonanceresonance andand massmass gapgap GoodGood signatures:signatures: signalssignals ofof partialpartial compositenesscompositeness GreatGreat signaturesignature ifif measurable:measurable: relativerelative raterate ofof γγγγ andand gluongluon gluongluon:: indicatesindicates warpedwarped extraextra dimensiondimension PlusPlus possiblepossible missingmissing energyenergy signaturesignature ifif infiniteinfinite extraextra dimensiondimension LotsLots ofof phenomenologyphenomenology MuchMuch stillstill toto bebe workedworked outout ButBut wewe reallyreally wantwant toto bebe ableable toto pinpin thisthis downdown EnteringEntering aa newnew eraera inin physicsphysics

EveryEvery timetime wewe’’veve exploredexplored smallersmaller oror largerlarger lengthlength scales,scales, wewe’’veve foundfound newnew phenomena,phenomena, newnew connectionsconnections ManyMany excitingexciting newnew ideasideas forfor whatwhat wewe mightmight discoverdiscover MoreMore connectionsconnections areare therethere——wewe justjust havehave toto findfind themthem SecretsSecrets ofof thethe universeuniverse areare aboutabout toto unravelunravel HiddenHidden richesriches inin thethe universeuniverse