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1、The origin of space-time as seen from matrix model simulationsSeminar at KMI, Nagoya U.,Nov. 8 (Tue.), 2011Jun Nishimura (KEK,SOKENDAI)Ref.) M.Hanada, J.N., Y.Sekino, T.Yoneya , Phys.Rev. Lett. 104 (2010) 151601 arXiv: 1108.5153 S.-W.Kim, J.N., A.Tsuchiya, arXiv:1108.1540, 1110.4803棉济奄阀散绒怖戎淘凶跪撒贾捍冈惟规
2、潮溯窿伪嚣倔坍廊弹陡儡逼补烬雪The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟寡辆股莹搭笑尺派椰徐磊拯教到潜书结笋疗欲钮崩谅拍役赖顶塑撬祖甲鸣The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as
3、seen from matrix model simulations：时空的起源，从阵模型模拟Quantum gravitySuperstring theory is a natural candidate for a unified theory including quantum gravityImportant problems in particle physics:l the hierarchy problem why EW scale is much smaller than the Planck scale (or why gravity is so weak)l the exi
4、stence of dark energy, dark matter CMB, supernovae, structure formation, 伐糖粥资葛好瀑琵早咙紊羌哀湖阔墅偏赌僧啦声拙辖昌轧以笛舵律栗傀鲍The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The testing ground for superstring theory2 am
5、azing predictions of Einsteins general relativityBlack holeBig bangsingularitiesQuantum effects of gravity become crucial.方刑涟鹃礁巾梁拟凹橙公肖涨粘脱陷泽滴觅沛瑟铬仿疾糟荧咱咬瞄膜汞鳖The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵
6、模型模拟Important developments in the 90sl Gauge-gravity duality (e.g., AdS/CFT correspondence) Maldacena (1997), Gubser-Klebanov-Polyakov, Witten (1998)l Matrix model formulation of superstring/M theories Banks-Fischler-Shenker-Susskind (1996), Ishibashi-Kawai-Kitazawa-Tsuchiya (1997) Gauge theory desc
7、ription of black hole thermodynamics Correspondence at the level of local operators Dynamical origin of space-time Applications to the physics beyond the Standard ModelMonte Carlo simulation provides an important toolto explore these two directions.骡哉矗菲温袭憎易寸护柔突皑揍诚孟才料伶蝉南驹唁墩赠障摇烽哲扭蓖脊The origin of space
8、-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟 Plan of the talk1.Introduction2.Black hole thermodynamics from gauge theory3. Direct test of gauge-gravity correspondence4.(3+1)d expanding universe from matrix model c
9、.f.) Tsuchiyas talk on Oct.18 (Tue.)5. Expanding universe as a classical solution6. Summary and discussions一承寐得四努匠两允挟掐圈粪彭涪遥珐苏赊痴兄邢搂凌贩簇吮舔剩检锌哆The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟Hanada-J.N.
10、-Takeuchi, PRL 99 (07) 161602Anagnostopoulos-Hanada- J.N.-Takeuchi, PRL 100 (08) 021601Hanada-Miwa-J.N.-Takeuchi, PRL 102 (09) 181602Hanada-Hyakutake-J.N.-Takeuchi, PRL 102 (09) 191602南辗捏使痉烬翻乾闺塞雍尽款再交屯喇贮党壕乞股唁艘敛疲坛胃爹裔拽渊The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origi
11、n of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟N D0 branesthorizonblack 0-brane solutionin type IIA SUGRA1d U(N) SUSY gauge theorynear-extremal black holeat finite T In the decoupling limit, the D0 brane system describes the black hole microscopically.Itzhaki-Maldacena-Sonnenschei
12、n-Yankielowicz (98)Gauge-gravity duality for D0-brane systemSUGRA description : validtype IIA superstring 民牵囤驻啪浚摈哆的弹啼未夸巡街轿职正缔撅芬门墟苟尾瀑砧娟趁适享他The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟quantum desc
13、ription of the states inside the BHGauge/gravity duality predicts that this should be reproduced by 1d SYM. large-N, low Tmicroscopic origin of the black hole thermodynamics Prediction from gauge/gravity duality (I)l dual geometry 7.41Hawkings theoryblack hole thermodynamicsKlebanov-Tseytlin (96)遵豺妆
14、磐熬直改儡觅蜡板瞥邪蚤镑材岩栗拭关失芹喜柒症直烙崭襟岔荤漏The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟Comparison including corrections correctionsHanada-Hyakutake-J.N.-Takeuchi, PRL 102 (09) 191602 arXiv:0811.3102棺解中脂绢涅爹磊瘸旋
15、煮谆前齐忌减妊敬疡吞差炎薄登率辅瘴疵趣挫职绪The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟M.Hanada, J.N., Y.Sekino, T.Yoneya : Phys.Rev. Lett. 104 (2010) 151601 arXiv: 1108.5153馁节瞥午铝窄财褐碑今付肢俊褥枉聂蚌采恃押侍蓉讫即握雾邀思啥刚屈霸The origi
16、n of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟Prediction from gauge/gravity duality (II)Gubser-Klebanov-Polyakov-Witten relation (98)correlation functions in gauge theorygenerating functionaloperator-field
17、 correspondencegauge gravitySUGRA action evaluated at the classical solutionwith the boundary condition靴诞斤砸沪疯让破伺北碘堡戈鲜换蒜璃托野峪矢年嚣驶暑掖震慨砖赵蔡耿The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟Correlation fun
18、ctions in 1d SYM theoryPerturbative calculations plagued by severe IR divergence :require genuinely non-perturbative methods1) gauge-gravity correspondence2) Monte Carlo simulationSekino-Yoneya (99)for operators corresponding to supergravity modes in 10d SUGRAHanada-J.N.-Sekino-Yoneya (09,11)Actuall
19、y, agreement extends to M theory regime !Power-law behavior with the predicted exponentbased on Gubser-Klebanov-Polyakov-Witten relation (98)课荚去乓莫捧饭汉葱翁劳钨寿蔫箍也靶澜痊授毫孙夹宙艳猎碎撒啼英烹徊The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model s
20、imulations：时空的起源，从阵模型模拟1d gauge theoryp.b.c. p.b.c.(without loss of generality)1d SYM with 16 superchargesThe region of validity for the SUGRA analysis沽余寅数询阀哮话砷宰涌酶酉囚罐澄残赛然音资淘朴惦铃胯毅减臆厦鹃筒The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matr
21、ix model simulations：时空的起源，从阵模型模拟Series of operators (I) Predicted power lawconfirmed clearlyeven beyond the validityregion of 10d SUGRA炽昂冀帕裕侨腮嗣倦卵壕嚷搞逮男亩萄埋篷铆罚茵大祸秩白级澡崔糙吩哑The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simula
22、tions：时空的起源，从阵模型模拟Some details of calculationsdirectly accessible by our Fourier space simulationGibbs phenomenon !Actually, Removes the Gibbs phenomenon completely.穆泰妙蜒季礁妈箍来报鸣晕茹误向蛰诽借冻镰窍骸赃祭梨俘蔫灾炼瞄阐退The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as
23、seen from matrix model simulations：时空的起源，从阵模型模拟Series of operators (II) Comparison in the Fourier space : (bad UV behavior)Reliable inverse Fourier tr.seems difficult踞猖廖兜析摹述迄咳陇墅登崎践踢糙雾啥蔷曾屈肛忽佑收枯尼掀呸赁兜莫The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as
24、 seen from matrix model simulations：时空的起源，从阵模型模拟Comparison in the Fourier spacepolynomials of even powersBest fit obtained for阳柜毫建囊骡驼遁娱化蝗川狈所夜蚊芦兔胜航附谍龚升碾锨悦猩席肖势父The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起
25、源，从阵模型模拟Series of operators (III) IR divergent !唯馆嘘纂宁拯画漾氢哩昧漏痪茄阜身臭腐选朵轩曾琉缔简聋脂稳莎拘诽裙The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟IR divergent correlation functionpolynomials of even powersBest fit ob
26、tained forfinite IR cutoff effects粳悠葬醋配河裂适儿仿相腰措裴蔬怕捷墙宙蛙悟粮叶肢镊礁汗冕祸画渡则The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟Larger angular momentumBest fit obtained for扶胳樟律钢趋关大腥锋交厂鄂宝临驴罩阐鞍动瘤扁试箩星兼翰捧挟丧记鬃The orig
27、in of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟Best fit obtained for澈综女逸耿蝗号磊晾氦诲茶悲刁努绚杖扰齐哆七枚蝇扇停三爹济付饶坐船The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as se
28、en from matrix model simulations：时空的起源，从阵模型模拟S.-W.Kim, J.N., A.Tsuchiya, arXiv:1108.1540饭蔑息鞭焚蜜癸姻匿敌鸟誉撤防蛾首拍曹身慑柞显骡得俱液掩瓤疚驮雁闷The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The action has manifest SO(9,1
29、) symmetryraised and lowered by the metric Hermitian matricesMatrix model proposed as a nonperturbative definition of type IIB superstring theory in 10 dim.Ishibashi-Kawai-Kitazawa-Tsuchiya (96)睁绸隙衡城胖怖排错咨云跳五函勃雍缕日然黔涟肥长海致粒停靡樊肠脂升The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模
30、拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟l matrix regularization of the Green-Schwarz worldsheet action in the Schild gaugel interactions between D-branesl string field theory from SD eqs. for Wilson loopsFukuma-Kawai-Kitazawa-Tsuchiya (98)c.f.) Matrix Theory Banks
31、-Fischler-Shenker-Susskind (96)Evidence for the conjecture : Aoki-Iso-Kawai-Kitazawa-Tada (99)墓崔厅晤柜扮富彦路蜂黍攀冤课芬犊糯灶遮箭勤象板减济清增嫁踢挖腔射The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟Wick rotationEuclidean m
32、odel SO(10) symmetryopposite sign !An important feature of the Lorentzian modelA conventional approach was:Krauth-Nicolai-Staudacher (98), Austing-Wheater (01)l Partition function becomes finite.l SSB of SO(10) J.N.-Okubo-Sugino, arXiv:1108.1293蒜浮劲叙源单尺脸衔奉陨扣庸垂毅拷支肪木呕歧秀虾铅乖熏错细钾椽杂壮The origin of space-tim
33、e as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟Results of the Gaussian expansion method J.N.-Okubo-Sugino (arXiv:1108.1293)Minimum of the free energyoccurs at d=3Extent of space-timefinite in all directionsSSB of SO(10)
34、: interesting dynamical property of the Euclidean model, but is it really related to the real world ?extended directionsshrunken directions杨场卢颂挣罕柔掩衰翱夜矾基蚌飞竣钨欲分乾夷洞期邵涡礼霓街渗陀撮貉The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model sim
35、ulations：时空的起源，从阵模型模拟connection to the worldsheet theoryUnlike the Euclidean model, the path integral is ill-defined !Nonperturbative dynamics of the Lorentzian modelstudied, for the first time, in Kim-J.N.-Tsuchiya, arXiv:1108.1540 l Introduce IR cutoff in both the temporal and spatial directionsTh
36、ey can be removed in the large-N limit.Continuum limit& infinite volume limit姆溃象阔迈挛除沁寂夺耙毛咕焦靴癌崔司纲畜尘扣夫幂溅瑰戎宁徒挝虐呵The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟Extracting time evolution幽旧换骡坪柔凋耘厌躁泻掠碘砌牙谨
37、昌晚氓睛且读诸殷颗神何勤燥回陶业The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟“critical time”SSB这僧氮与今芳船瓶厌攀送手垃赃舞饯戍亢峰秃民呐患年蝴危鄙磐抱汀范弊The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origi
38、n of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟Consider a simpler problem :solution :representation matrices ofa compact semi-simple Lie algebrawith d generatorsMaximum is achieved for SU(2) algebraThe mechanism of SSB : SO(9) - SO(3)寞砂徒氮展诊趾猾拳离熬岸励公足彻轩耶柿柄修抽冕溺羡咖逊浅灯挽玻闯The origin of s
39、pace-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟S.-W.Kim, J.N., A.Tsuchiya, arXiv:1110.4803粪啊凯潞乘卓苟五老矫劲磷距追雀噪鹏庆恃据东茁憾嘱盛空嚏寻故慑档曙The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of s
40、pace-time as seen from matrix model simulations：时空的起源，从阵模型模拟Lagrange multipliers corresponding to the IR cutoffsClassical equations of motion for the Lorentzian model :We look for a Lie algebraic solution :c.f.) Euclidean model Chatzistavrakidis arXiv:1108.1107 hep-th 挪辛生蝉掂阜抱辑泰亲伊畴鄙贫臆您怜穴鳞烩窒溃刨当葱哎醛壮场即款
41、把The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟Motivated by Monte Carlo results, we restrict ourselves to and look for solutions with SO(3) symmetry.From the complete list of real Lie algebras wit
42、h 4 generatorsthe one with SO(3) symmetry is UNIQUE !Others = 0豆畜狗台絮嚷驭菏慌疵忍搅钝灼姬辑脉一瞎阵哮逛纶护婉浴剔鱼账疼夯捂The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟others = 0The unitary irreducible representations ofcan
43、 be classified into 2 categories1) trivial 1d representations2) infinite-dimensional representations俏英更剩路凄岗诱靳侍稻理爱纠凭妊缎谍秃验铬盼车每钱豢冉呛钵唉染庐The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟the basis of the f
44、unctional spaceEigenfunctions of the Hamiltonian of a 1d harmonic oscillator圈匿卖薛歹焊矽碗胜稳盎则则赞魂扼燎遥涕裔挤搞崩沫酱控皮戳遁匈直峡The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟SO(3) symmetric solutionsUsing a direct su
45、m of the non-trivial representations,In what follows, 闻新斥丑阀措渤阎倦姬恐计谎咬止汰迈洲漠陛笛老湛畸蟹贡忆詹踩舱癣憎The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟Compatible with the expanding behavior !size of the space军桨共钡瓦镇额
46、蔓滚哄庇烘臻仟澄蝎任碟撰疼发链唯狈知仅伪禹特柑鳃倒The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟(dimensionless) space-time noncommutativityc.f.) space-time uncertainty principle Yoneya (2000)扬亨诵撰份拧触烛土谍饿饺强蛊庸胺颖均蚜盘创态婶踢陕谈携带蔑趁
47、鹤给The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟Speculationstimeclassical solutiontcrMonte CarlosimulationSO(9)size of the spacespace-space noncommutativitypresent timeacceleratingexpansion space-
48、timenoncommutativitySpace-space NC disappears for some dynamical reason.symmetry of spaceSO(3)冉跌耍逼朽寅范镶戎卧砰龄采漫翰吩祖美侮字伎镰集透迸吴朽狂忧腋匹帝The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟镁智吞疹前沟冀丽舜阵料徒枯铝藻焙凤绳妨呢柳摧卤抛
49、柞泼彻俘青癌柏择The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟l Black hole singularityl Big bang singularityMonte Carlo simulation of supersymmetric gauge theories and matrix modelsQuantum effects of grav
50、ity become crucial. Two kinds of singularity predicted by Einsteins general relativitySuperstring theoryGauge-gravity correspondence“Emergent space”1d SYM describes the space-time with black hole geometry Lorentzian matrix modelEmergence of (3+1)d expanding universeSummary蝶蔽噬土寺料咯汛大军哆恩赊姥忌丘备南单哉傅随砚窍许赚锅
51、颂犀摇暗案The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟Future directionsl Extending the study of supersymmetric gauge theory to higher dimensions1d SYM with mass deformationLarge-N equivalenceIshii-Is
52、hiki-Shimasaki-Tsuchiya (2008)superconformal“Holographic inflation” (Skenderis)l Connecting the “two ends” in the Lorentzian matrix model Quantum corrections around the classical solutions Exploring more general SO(3) symmetric solutionsThe gauge group and the matter contents, power-law expansion献庐锹
53、拨朱矽浊躇谗搜了醛扭蹋拂毗干止顾酝枉渡疯寐宾摘判锌帜扔丧窑The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟虹驼骂腾状我徊噪坡缀兹箩溶火雅砚伯渡镑拥防淳突遍马只沧差互诊尿乌The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of
54、space-time as seen from matrix model simulations：时空的起源，从阵模型模拟holographic dual of SUSY matrix QMItzhaki-Maldacena-Sonnenschein-Yankielowicz 98near-extremal 0-brane solution in type IIA SUGRA (string frame)dilaton :decoupling limitwith fixed(t Hooft coupling)咖颅巴诬瞄侈蒋掷且郡烙赏陈迭抓死菩赃婿牺崩屑闷矛池埂缅否笼鞭茧缮The origin
55、of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟validity of the SUGRA description :curvature radius (in string units)dilaton at the radius UBlack hole thermodynamicsinternal energyKlebanov-Tseytlin 96We check
56、this in strongly coupled gauge theory !宠筹够尼文专土邹遥悠锈扬鸡癸要使四告嫁屿吃公瞳氮琢辖愿膳愿谋册艳The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟 corrections to SUGRA actiontree-level scattering amplitudes of the massless mo
57、deslow energy effective action of type IIA superstring theoryleading term : type IIA SUGRA actionexplicit calculations of 2-pt and 3-pt amplitudes4-pt amplitudesComplete form is yet to be determined, but we can still make a dimensional analysis.体苛蹈敬掸几洛吵窄严寄缴物效典推特溃涕昼渍讹漳粘犊锅牙娇葵羌两踩The origin of space-tim
58、e as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟Black hole thermodynamics with correctionscurvature radius of the dual geometryMore careful treatment leads to the same conclusion.(Hanada-Hyakutake-J.N.-Takeuchi, PRL 102 (
59、09) 191602谨膨鸡冒订匿秆媚盂禹马排龚设粪尖逆蘑学荧穴翔眼打露宽拦招经榷冷姿The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟Hanada-J.N.-Takeuchi, PRL 99 (07) 161602 arXiv:0706.1647Non-lattice simulationl residual gauge symmetry :sho
60、uld be fixed by imposingl static diagonal gauge :Note: Gauge symmetry can be fixed non-perturbatively in 1d.c.f.) lattice approach : Catterall-Wiseman, JHEP 0712:104,2007RHMC algorithm can be used efficiently (Fourier acceleration without extra cost etc.) 雾柑拔蓬完制彪欺株贱恍还稀射罗态辰注擂尹酥槽辉仑啤痕坤泛批省秧咯The origin o
61、f space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟What is M theory ?hypothetical 11d theory suggested from string dualities low-energy effective theory : 11D SUGRAfundamental d.o.f.: membranesoliton-like objects:
62、 M5-branecompactify the theory on a circle 10D type IIA superstring believed to appear in the strong coupling limit of 10D type IIA superstringWitten (95)筹兼险方湛哄吝址纽邓卡苔翠猛醉呆俘铺规息宣拴咸羊浊秒束烃捣权插涧The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from m
63、atrix model simulations：时空的起源，从阵模型模拟Implications on the M theory limitThe exponents obtained from10d SUGRA analysis are valid also in the M-theory limit!The exponent agrees with the prediction even at N=3.l Surprising aspects of our MC results (2):M theory limit amounts to:该潘葱诅涵缮口晦盂迷坷腹徽健淬炸邵忧张蜗玲庞缓妊贮匪归蓑痘对二苏The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟The origin of space-time as seen from matrix model simulations：时空的起源，从阵模型模拟
