The wonders of supersymmetry: from quantum mechanics, topology, and noise, to (maybe) the LHC Erich Poppitz http://www.slac.stanford.edu/spires/hep/ HEP Search High-Energy Physics Literature Database find title SUPERSYM# or title SUSY# or title MSSM or title NMSSM or title NNMSSM Nov. 21, 2005 Paper 1 to 25 of 13979 Oct. 18, 2007 Paper 1 to 25 of 15656 what is supersymmetry? what is it good for? why we have studied it for so long? (will we ever stop?) supersymmetry is a quantum mechanical space-time symmetry, which relates bosons and fermions curiously, it was not discovered in quantum mechanics first, but in string theory and quantum field theory Ramond 1971 Golfand, Likhtman 1972 Wess, Zumino 1974 nevertheless, some of its most important applications to date involve quantum mechanics Witten 1981 moreover, supersymmetric quantum mechanics has all features that make it clear why supersymmetry is interesting to particle physicists, as well as to other fields the harmonic oscillator in quantum mechanics, we know that implies bosons: commutation relations between creation and annihilation operators energy spectrum of bosonic oscillator what are fermions? they obey Pauli principle! explicitly: fermions: anti-commutation relations between creation and annihilation operators the -1/2 may look cooked-up, but it comes from quantizing the Dirac equation+C-symmetry we’ll simply define fermionic oscillator that way energy spectrum of fermionic oscillator add them up: the supersymmetric oscillator Proof: introducing: the supersymmetry generators this is not as silly as it looks! we just found one of the simplest SUPERALGEBRAS! superalgebra has even (H) and odd (Q) elements, obeying commutation or anticommutation relations we know that Hamiltonian generates time translations - - took square root of time translations! similar to the Hamiltonian H, the supersharges Q can be thought as of generating translations in a “fermionic dimension” of spacetime, making it thus into a superspace Physica 15D (1985) 289-293 North-Holland, Amsterdam Physica 15D (1985) 289-293 North-Holland, Amsterdam STUPERSPACE STUPERSPACE V. GATES}-, Empty KANGAROO:~, M. ROACHCOCK*, and W.C. GALL* California Institute of Technology, Pasadena, CA 91125, USA Pentember, 1999 V. GATES}-, Empty KANGAROO:~, M. ROACHCOCK*, and W.C. GALL* California Institute of Technology, Pasadena, CA 91125, USA Pentember, 1999 We prove, once and for all, that people who don't use superspace are really out of it. This includes QCDers, who always either wave their hands or gamble with lettuce (Monte Zuma calculations). Besides, all nonsupersymmetric theories have divergences which lead to problems with things like renormalons, instantons, anomalons, and other phenomenons. Also, they We prove, once and for all, that people who don't use supercsapna'cte hairdee really from ogravityut of it. forever. This in cludes QCDers, who always either wave their hands or gamble with lettuce (Monte Zuma calculations). Besides, all nonsupersymmetric theories have divergences which lead to problems with things like renormalons, instantons, anomalons, and other phenomenons. Also, they can't hide from gravity forever. Whatever it is, I'm against it. Groucho Marx Whatever it is, I'm against it. Groucho Marx Supersymmetry is the wave (particle) of the [11], Reaganomic symmetry [12], tensor arithmetic future in high energy physics [1]. Even people who [13], and maiden forms [14]. It is also a very Supersymmetry is the wave (particle) of the used[11], to d Ro esatguaffn olimkeic I NsyTmEmSeTtrIyN [E1s2 ],a tnedn spoarn aarvitihsimoent ic compact notation: e.g., a superfield equation ~ = future in high energy physics [1]. Even people who are n[13],ow daonidn g msuaipdeernlN fToErmSTs I[14].NEs [I2t ] i(sG aUlsTo sau pvee) ry Dq, (as in, e.g., a Dq~ of relief) would in compo- used to do stuff like INTESTINEs and panavision and csoumpeprapcat nnaovtiastiioonn : [3e].g. .G, ar asvuiptyer fpielodp leeq uaartei ornu n~- = nents be [15] are now doing superlNTESTINEs [2] (GUT supe) ningD oqu, t( aosf inid, eea.sg,. , tao oD. qA~ lotfh oreulgiehf ) twheoyu ldh aivne cpormop-o - and superpanavision [3]. Gravity people are run- nents be [15] gressed from classical calculations to medieval ones ning out of ideas, too. Although they have pro- qt + * ( & % / 1 3 7 . ) f d~ ~ [4], modern calculations are impossible without gressed from classical calculations to medieval ones qt + * ( & % / 1 3 7 . ) f d~ ~ [4], modern calculations are impossible without supergravity due to the well-known X-ray diver- = lira e dx A FAn(J§°Kv/-5 gences [5]. (As we all know, X-rays travel along 13onzo --* college supergravity due to the well-known X-ray diver- = lira e dx A FAn(J§°Kv/-5 gences [5]. (As we all know, X-rays travel along parallel1 3olniznoe --s* ,college wh ich never diverge.) Also, super- • lx"°de'fTb • c ® (x, y, z)Sl/ parallel lines, which never diverge.) Also, super- symmetric theories are the most symmetric, which symmetric theories are the most symmetric, which makes •t lhx"e°mde 'ftThbe • pcr e®t t(ixe,s ty, , szo) Slt/h ey've got to be / _ $ - # ! ? ! . O ? ~ eo. makes them the prettiest, so they've got to be right. C/ _h$an- #ce!s? !a r.e. .t heyO'll? g i~v eo .c onfeynman, too, right. Chances are they'll give confeynman, too, since with 1073741824 + 1073741824 components Furthermore, component formulations leave out Furthermore, component formulations leave out components needed to make nice even numbers siwhilence abstract,with 1 0superspace73741824 is +quite 1073741824 a useful concept, com pwhenone nhandledts [6] withthe rcare'se no room left for quarks to be free [6] there's no room left for quarks to be free (miccromwapvoen esnetgsr engeaetdioend) t[7].o m ake nice even numbers like 1073741824 [16]. Superfields also allow the use (microwave segregation) [7]. Sulipkeer s1p0a7c3e7 4[188] 2i4s t[h1e6 ]g. rSeuapteersfti eilndvse anltsioo nal lsoinwc eth eth ues e of supergraphs [17], which give amazing cancella- Superspace [8] is the greatest invention since the wheeolf [s9u]p. eIrtg frapr hssu r[p1a7s]s, ewsh aiclhl ogtihve ra mapapzriongac chaensc etlola - tions like the l-loop vacuum bubble: tions like the l-loop vacuum bubble: wheel [9]. It far surpasses all other approaches to supersymmetry [10], like Chevrolet cohomologies sPuhpyseicar s15Dym (1985)me 289-293try [ 10], like Chevrolet cohomologies O = 0 . North-Holland, Amsterdam O = 0 . Physica 15D (1985) 289-293 ]'Jolly Good Fellow, supported in part by Ulysses S. Grant North-Holland, Amsterdam We use the following notation: Greek letters for ]'Jolly Good Fellow, supported in part by Ulysses S. Grant # 10036.W e use the following notation: Greek letters for # 10036. ~On leave of his senses. vile spinor indices, Roman letters for isospin in- ~On leave of his senses. vile spinor indices, Roman letters for isospin in- STUPERSPACE * Work supported by the U.S. Department of Momentum. dices, Cyrillic letters for vector indices, Hebrew * Work supported by the U.S. Department of Momentum. * Pedrimcaense, ntC aydrdirleliscs : l"eYttoeurrs Rfooyra l vHeicgthonre sisn"d. ices, Hebrew * Permanent address: "Your Royal Highness". letters for 10-dimensional vector indices, Roman V. GATES}-, Empty KANGAROO:~, M. ROACHCOCK*, and W.C. GALlLe*t ters for 10-dimensional vector indices, Roman CaliforniSa TInUstitPutEe oRf Technology,SPACE P asadena, CA 91125, USA 0167-2789/85/$03.30 © Elsevier Science Publishers B.V. 0167-2789/85/$03.30 © ElseviePre nStemcbieer, n19c9e9 Publishers B.V. (North-Holland Physics Publishing Division) (North-HVo.l lGaAnTdE SP}h-y, sEimcsp tPyu KbAliNshGiAnRg ODOi:v~i,s Mio.n R) OACHCOCK*, and W.C. GALL* We pCroavleif, oornnciea a nInd sftoitru all,te othfa tTechnology, people who dPona'sta usede nsau,p eCrsAp ac91125,e are really US Aou t of it. This includes QCDers, who always either wave their hands or gamble with lettuce (Monte Zuma calculations).Pentemb eBesides,r, 1999 all nonsupersymmetric theories have divergences which lead to problems with things like renormalons, instantons, anomalons, and other phenomenons. Also, they can't hide from gravity forever. We prove, once and for all, that people who don't use superspace are really out of it. This includes QCDers, who always Whaeteivtehre irt is,w aIv'me atghaienisrt it.ha nds or gamble with lettuce (Monte Zuma calculations). Besides, all nonsupersymmetric theories have divergences which lead to problems with things like renormalons, instantons, anomalons, and other phenomenons. Also, they Groucho Marx can't hide from gravity forever. Supersymmetry is the wave (particle) of the [11], Reaganomic symmetry [12], tensor arithmetic future in high energy physics [1]. Even people who [13], and maiden forms [14]. It is also a very used to do stuff like INTESTINEs and panavision compact notation: e.g., a superfield equation ~ = Whatever it is, I'm against it. are now doing superlNTESTINEs [2] (GUT supe) Dq, (as in, e.g., a Dq~ of relief) would in compo- and superpanavision [3]. Gravity people are run- Groucho Marx nents be [15] ning out of ideas, too. Although they have pro- gressed from classical calculations to medieval ones qt + * ( & % / 1 3 7 . ) f d~ ~ [4], modSeurnp ecraslcyumlamtioentsr ya rei si mtphoes siwblea vwe ith(opuatr ticle) of the [11], Reaganomic symmetry [12], tensor arithmetic superfguratvuirtye dinu eh tiog hth ee nweerlgl-yk npohwyns iXc-sr a[y1 ]d. iEvevr-e n pe=o ple wlirha o e dx[13], A FA n(aJ§n°dK v/m-5 aiden forms [14]. It is also a very 13onzo --* college genceus s[e5d]. t(Ao sd woe satlul fkfn loiwke, XIN-raTyEs StrTavIeNl Ealso nagn d panavision compact notation: e.g., a superfield equation ~ = parallaerl el ineosw, w dhoicihn gn esvuerp edirvleNrgTe.E) SATlsIoN, Esusp e[r2- ] (GUT supe) symmetric theories are the most symmetric, which • lx"°de'fTb • c ®D (qx, y(,a zs) Siln/ , e.g., a Dq~ of relief) would in compo- makeas ntdh emsu ptheer pparentativesits, ioson t[h3e]y.' vGe rgaovti ttyo pbe ople a/r_e $r-u#n! ?- ! .