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Home , Quantum chromodynamics

Supersymmetry and how it helps us understand our world

Spitalfields Day , and Unification, 8 October 2007

M. Shifman Theoretical Institute, University of Minnesota

M. Shifman What is ?

Supersymmetry, if it holds in nature, is part of the structure of space and time. In everyday life, we measure space and time by numbers, “The linear dimension of this building is 40 meters, its area is 1600 square meters.” Numbers are classical concepts. Our basic way of thinking about space and time has not been affected by physics revolutions of the 20th century: and Einstein’s relativity. x t,x,y,z t,x,y,z; θi { } −→ { α}

In 1+3 dimensions “” direction of the superspace y θ2 = 0 θ −→

Supersymmetry introduces, apart from the three obvious dimensions plus time, new “quantum” dimensions, not measurable by ordinary numbers. They are “quantum” (or “fermionic” dimensions, like the of the .

M. Shifman M. Shifman ✵ Particles vibrating in the new dimesnions look in detectors like new elementary particles. Thus, quantum dimensions would be manifested in the existence of new elementary particles, which would be produced in accelerators and whose behavior would be governed by supersymmetric laws. Supersymmetry entails that for every particle that has been found there are mirror particles that are identical in all respects except for their spin. of spin 1 — the , W, Z, and — have spin 1/2 partners called the photino, wino, and gluino. of spin 1/2 — and — have spin 0 partners called the sleptons and squarks.

∼∼∼∼ Fermion Fermions Bosons

e γ

Spin 1/2, 3/2, ... Building blocks of ... Spin 0, 1, ... mediators/helpers in Absolute individualists: delicate issues... Love to congregate and Pauli’s Exclusion Principle mimic each other: Huge ensembles -> Classical

M. Shifman Can there be any between bosons and fermions?

Golfand & Likhtman, 71 Wess & Zumino, 73

1970’s: YES!

M. Shifman E = mc2 Cultural icon of the 20th century

µ st Q¯ ˙ , Q = 2σ P Of the 21 ? { α β} αβ˙ µ

Defying the Coleman-Mandula theorem!

M. Shifman

M. Shifman ✵ ✵ ✵✵ ✵ ✵ ✵ ✵ ✵ ✵

✵ LHC ... ✵ ✵

SUSY or NOT? M. Shifman ✷✷✷ Why do we need SUSY ? ✷✷✷

Supersymmetric model-building A tool for solving otherwise unsolvable problems of

Hierarchy problem: Mpart 1-100 GeV strong dynamics while M 1019 GeV Planck ≈ Costs nothing; E ≈ 0 vac Cold Enormous progress since mid-1990’s! More efficient decoupling of high ▲▲▲▲▲▲▲▲▲ energies: Comes at a price ▲▲▲▲▲▲▲▲▲ Lots of problems + SUSY partners to be discovered M. Shifman Spontaneous symmetry breaking

magnon

=gapless excitation

Goldstone boson Goldstino Fermion

gravitino goldstino gravitino goldstino = massive gravitino

∼∼∼∼ M. Shifman ? 1 a µν a i b L = G G + λ¯D/ λ −4g2 µν 2 f gluon

gluino ∼∼∼∼∼∼ SUSY Yang-Mills supersymmetric gluodynamics

∼ ∼ ∼

M. Shifman A success of SUSY: gauge coupling unification ● We are here MPlanck

M. Shifman ✷✷✷ SUSY as a tool in strongly coupled gauged theories: QCD and the like ✷✷✷

Quantum Chromodynamics (QCD): • Quantum Theory of Strong Interactions of quarks and , • Interaction mediated by exchange of gluons • Gluons carry color charges;

Special Properties of QCD: • "," • Color Confinement: are always "white," • Linear potential between quarks.

M. Shifman QED 2

force 1/

QCD distance

▲▲▲▲▲▲▲▲▲ Nature keeps surprising us !!! ☞ Are we aware of precedents? ☞ Yes, the Meissner effect! 1930s, 1960s

Cooper pair condensate Abrikosov vortex (flux tube) →B → S N → →→ S N magnet magnetic flux magnet

Superconductor of Abelian ☚ the 2nd kind Dual Meissner effect for confinement conjectured

1970s

Mandelstam Nambu ‘t Hooft ✵ ✵ ✵ ✵ ✵ ✵ ✷✷✷ First demonstration of the dual Meissner effect: Seiberg & Witten, 1994 ✷✷✷

N=2 (extended) SUSY ➔ SU(2) →U(1), monopoles ➔

Monopoles become light ➔ N=1 deform. M condensatition ➔

U(1) broken, electric flux tube formed ➔ ☺☹ ☺☹ Abelian ... (Abrikosov) Meissner effect does take place: condensation of color charges (squarks) gives rise to non-Abelian flux tubes and confined monopoles. The very fact of their existence in = 1 supersymmetric QCD without adjoint scalars was not known previously. The N Meissner effect does take place: condensation of color charges (squarks) gives rise to analysis presented in Ref. [13] is naonna-lAybtiecliaannflduxistubbaessedanodncotnhfienefdacmtotnhoaptoletsh.eThe v=ery1 fact of their existence in N theory under consideration can be ob=ta1insuepdersstyamrtminetgrifcroQmCD wi=tho2uSt QadCjoDintinscawlahriscwhatshneot known previously. The N N ’t Hooft–Polyakov monopoles do eaxnisatly,stishrporeusgenhteadcienrtRaeifn. [l1im3]iitsinagnaplyrtoicceadnudries ablalsoewdionng the fact that the = 1 theory under consideration can be obtained starting from = 2 SQCD in whNich the one to track the status of these monopoles at various stages (analogous to the onNe ’t Hooft–Polyakov monopoles do exist, through a certain limiting procedure allowing deMscerisisbneedr eaffbecotvdeoeasntdakseupmlacme:acroizneddensiantiFonigo.f c1o)l.or charges (squarks) gives rise to non-Abelian flux tubes and confined moonneoptoletsr.acTkhtehveersytaftaucst of tthheeisreemxisotneonpceoliens at various stages (analogous to the one T=h1e sMupemrsyomdmelestrhicarQeCsDmwainthyofuetaatdduejorsicenrstibwsecdaitlaharbstohwveaesIanSnoSdt skmunmaowgmnaeprtirziecevditohuinesloyF.riygT.h1Ie).will return to N thaisnaflayscits lparteseern.teNdoinwRIefw. o[1u3l]dislaiknealyttoicnTaonhtde iMsthbamatsoedndeoolnnsh-tBahrPeesSfamcfltaunthxyafteuatthbueersesiwn=itt1hhethme IeStSamstaagbnleetic theory. I will return to theory under consideration can be obtatinheisd fsatcatrtliantgerfr.oNmow I=w2oSuQldClDikeintwo hnNiochtetthheat non-BPS flux tubes in the metastable vacua of the SO(Nc) ISS theory with Nc +N 4 flNavors were found by Eto et al. [14]. ’t Hooft–Polyakov monopoles do exist, tvharcouuagohfathceer−StaOin(Nlim)itIiSnSgtphreoocreyduwriethallNow+inNg 4 flavors were found by Eto et al. [14]. In a parallel consideration, they made one extra cstep on the way cfrom the SU(Nc) one to track the status of these monopoles at various stages (analogous to the one − ISS magnetic theory towards theInMa pmaroadllell.coTnshideeyragtiaoun,gtehdeythmeadbeaornyeonextUra(1s)t.ep Tonhethe way from the SU(Nc) described above and summarized in FiIgS. S1)m. agnetic theory towards the M model. They gauged the U(1). The U(N)Thme aMgnmeotdiecl sthhaeroesrymaonbytfaeaintuerdesiUwni(tNthh)tihsme waISgaSnyemtisacugtnphepetiocrrtythseoobflrtuya.xinIewtduilblinreestthuiirnsnwttoahye smupeptoarsttsaflbulxe tubes in the metastable vatchuisafa[c1t4l]a.ter. Now I would like to notveatchuaat [n1o4n].-BPS flux tubes in the metastable vacua of the SO(N ) ISS theory with N +N 4 flavors were found by Eto et al. [14]. The M modelc can be regardedc asTt−hheeMfirmstodcoelucsainn boef rQegCarDdesdinascethtehfiersatdcjoouisnint fiofeQldCsD since the adjoint fields tyIpnicaaplaorafllel co=nsid2eratrieone, ltihmeyinmaatdeedtoyinpneiceatxhltirosaf stthepe=oorny2.thaerEewveaelyinmfritnohmatoetudhgehinSUstu(hNipsce)trhseyomrym. eEtvreyn itshough supersymmetry is ISS magnetic theory towards the M model. TheNy gauged the baryon U(1). The considerablNy weakened, the overaclolnsqiudearlaitbalytivweeapkeincteud,rethseuorvveirvaells.quTalhitiastivise ppircotubraebsluyrvives. This is probably U(N) magnetic theory obtained in thiosnweaoyfstuhpepmorotstfliumxptourbtaesntinfinthdeinmgsetaatsttahbelecurrent stage. onveacoufa t[1h4e].most important findings at the current stage. Can a dual of the M model be identified? If yes, this would be equivalent to the The M model can be regarded as the first cousin of QCD since the adjoint fields Can a dual of the M model bediedmeonntsitfiraetdio?nIoffytehse,ntohni-sAwbeoluialnddbuealeMqueisvsanleernetffteocttihne = 1. detmypoicnasltorfation= o2f atrheeelnimonin-aAtebdeliniatnhids utaheloMry.eisEsvneenrtehffouegcht siunpersy=mm1e.try is N considerablNy weakened, the overall qualitative pic1994ture -psurveisenves.t: TInhNi sseais rpcrohb aofb lynon-Abelian dual

one of the most important findings at t3he cuDrrenutaMeissnstlaigze.inegr e(ffaelcmt (noosn-At)belMian mfluxo dtubeel s) ▲ Can a dual of the M model be identified?MIf yes, this would be equivalent to the 3demoDnsturataiolniozf ithne gnon-(Aabellmian odusaltM)eissner effmectoinde=l 1. I started my talk frNom ISS who slightly mass-deformed SQCD. This small deforma- tion led to drastic consequences in the infrared-free magnetic dual theory: emergence I started my talk from ISS who slightly mass-deformed SQCD. This small defInotremrnaa-l d.o.f 3 Dualizing (almost) MoAfuzzia mn oetno -asdlu, peelrsymmetric metastable . tion led to drastic consequences inShthifmaneItintu f&rna Ysrueondug-tfrtNhoen-Aaetmbelfuiaanrgt shntreeinrtgqicuidteuamliltdhdeoefroyr:meamtioenrsgoefntcheis “electric” theory result Hanany & Tong ofIastnarotned-smuypetarlskyfmrommeItSrSicwhmoestliagshttalyibnmleaasvdsau-dacelufo“urmmmae.gdneStQicC”Dt.hTeohriys swmhaicllhdiesfovremrya-close to the M model discussed above. It tioInt lteudrtnosdroausttictchoantseqfuuernthceesrinqtuhieteinpfmrreasireledrdv-edfrseeaefolmlrsmaaglanieetntiiotcnfdesuaatoulfrthetsehooirsfy:t“heemleMecrtgrmeincoc”deetlh. eory result of a non-supersymmetric metastable vacuuSmh.ifman and Yung considered [15] = 1 SQCD with the gauge U(Nc) in a dual “magnetic” theory which is very close to the M model disNcussed above. It ☛an SU(2)d N di+ag Nbrokqenua ornk thefla vsotrrinsg( Ndow

7 7 Conclusions/Predictions:

☺ Most likely, SUSY will be discovered at LHC

☺ In any case, SUSY-based methods will proliferate

M. Shifman