M理论：所有超弦之母.doc

M理论：所有超弦之母 An introduction to M-Theory对M理论简介 Every decade or so, a stunning breakthrough in string theory sends shock waves racing through the theoretical physics community, generating a feverish outpouring of papers and activity.每10年左右，一个惊人的突破，在弦理论发送冲击波通过理论物理学界的比赛，产生的文件和活动的狂热爆发。 This time, the Internet lines are burning up as papers keep pouring into the Los Alamos National Laboratorys computer bulletin board, the official clearing house for superstring papers.这一次，互联网线烧起来的文件保存到洛斯阿拉莫斯国家实验室的计算机公告板，官方结算所浇筑超弦理论文件。 John Schwarz of Caltech, for example, has been speaking to conferences around the world proclaiming the “second superstring revolution.” Edward Witten of the Institute for Advanced Study in Prince- ton gave a spell-binding 3 hour lecture describing it.约翰施瓦茨美国加州理工学院，例如，已被周围的会议发言，宣布“第二超弦理论革命的世界。”爱德华王子在吨威滕高等研究院发表了神魂颠倒，3个小时的演讲描述它。 The after- shocks of the breakthrough are even shaking other disciplines, like mathematics.离职后的突破冲击，甚至动摇，如数学等学科。 The director of the Institute, mathematician Phillip Griffiths, says, “The excitement I sense in the people in the field and the spin-offs into my own field of mathematics have really been quite extraordinary.该研究所所长，数学家菲利普格里菲思说：“我的兴奋感在外地的人，到我自己的数学领域中的副产品.真的是很了不起的。 I feel Ive been very privileged to witness this first hand.”我觉得我已经很荣幸地见证这个第一手资料。“ Cumrun Vafa at Harvard has said, “I may be biased on this one, but I think it is perhaps the most important development not only in string theory, but also in theoretical physics at least in the past two decades.” What is triggering all this excitement is the discovery of something called “M-theory,” a theory which may explain the origin of strings. Cumrun哈佛大学瓦法说，“我可能是有偏见的这一个，但我想这也许是不仅在弦理论的最重要的发展，但至少在过去20年在理论物理也。”什么是触发所有这是兴奋的事发现所谓的“M -理论”的理论可能解释字符串的来源。 In one dazzling stroke, this new M-theory has solved a series of long-standing puzzling mysteries about string theory which have dogged it from the beginning, leaving many theoretical physicists (myself included!) gasping for breath.在一个令人眼花缭乱的行程，这个新的M -理论，解决了约弦理论，从一开始就一直困扰着它的长期令人费解的奥秘系列，使许多理论物理学家（包括我自己！）喘气。 M-theory, moreover, may even force string theory to change its name. M理论，而且，甚至可能迫使弦理论改变其名称。 Although many features of M-theory are still unknown, it does not seem to be a theory purely of strings.尽管M理论的许多功能仍是未知，它似乎并不单纯是一个理论的字符串。 Michael Duff of Texas A & M is already giving speeches with the title “The theory formerly known as strings!” String theorists are careful to point out that this does not prove the final correctness of the theory.迈克尔德克萨斯AM达夫已经给的标题“前身为字符串！”弦理论家已知的理论发言非常谨慎指出，这并不能证明这个理论的最后的正确性。 Not by any means.不以任何方式。 That may make years or decades more.这可能使年或20年以上。 But it marks a most significant breakthrough that is already reshaping the entire field.但是，它标志着一个最重要的突破，已经重塑整个领域。 Parable of the Lion狮子的比喻 Einstein once said, “Nature shows us only the tail of the lion.爱因斯坦曾经说过，“大自然显示我们只狮子的尾巴。 But I do not doubt that the lion belongs to it even though he cannot at once reveal himself because of his enormous size.” Einstein spent the last 30 years of his life searching for the “tail” that would lead him to the “lion,” the fabled unified field theory or the “theory of everything,” which would unite all the forces of the universe into a single equation.但是，我并不怀疑，狮子属于它，即使他不能马上透露，因为其庞大的规模自己。“爱因斯坦花了30年的岁月，为”尾巴“，将带领他的”狮子搜索， “传说中的统一场理论或一切的理论”，“这将团结成一个方程所有的宇宙力量。 The four forces (gravity, electromagnetism, and the strong and weak nuclear forces) would be unified by an equation perhaps one inch long.这四种力（重力，电磁，强，弱的核力量）将统一由一个公式也许一英寸长。 Capturing the “lion” would be the greatest scientific achievement in all of physics, the crowning achievement of 2,000 years of scientific investigation, ever since the Greeks first asked themselves what the world was made of.捕获的“狮子”将是最伟大的物理学所有的科学成就，科学调查的2000年的最高成就，自从希腊人第一次问自己，世界是什么组成的。 But although Einstein was the first one to set off on this noble hunt and track the footprints left by the lion, he ultimately lost the trail and wandered off into the wilderness.但是，尽管爱因斯坦是第一个启程的这一崇高的狩猎和跟踪的狮子留下的脚印，他最终失去了线索和漫步到旷野关闭。 Other giants of 20th century physics, like Werner Heisenberg and Wolfgang Pauli, also joined in the hunt. 20世纪物理学的其他巨头，像维尔纳海森堡和沃尔夫冈泡利，也加入了狩猎。 But all the easy ideas were tried and shown to be wrong.但是，所有的想法很容易被审判，并证明是错误的。 When Niels Bohr once heard a lecture by Pauli explaining his version of the unified field theory, Bohr stood up and said, “We in the back are all agreed that your theory is crazy.当尼尔斯玻尔曾经听取了泡利的演讲，解释他的统一场论的版本，玻尔站起来，说：“我们在后面都同意你的理论是疯了。 But what divides us is whether your theory is crazy enough!”但我们的分歧是，是否你的理论是疯了够了！“ The trail leading to the unified field theory, in fact, is littered with the wreckage of failed expeditions and dreams.步道领导的统一场论，其实，充满了失败的探险和梦想的残骸。 Today, however, physicists are following a different trail which might be “crazy enough” to lead to the lion.然而，今天，物理学家是不同的线索后，这可能是“疯狂”，足以导致狮子。 This new trail leads to superstring theory, which is the best (and in fact only) candidate for a theory of everything.这种新的线索导致超弦理论，这是最好的（实际上为一切理论只）候选人。 Unlike its rivals, it has survived every blistering mathematical challenge ever hurled at it.与其竞争对手不同，它已经历过的挑战都起泡数学在它扔。 Not surprisingly, the theory is a radical, “crazy” departure from the past, being based on tiny strings vibrating in 10 dimensional space-time.毫不奇怪，这个理论是一个激进的，“疯狂”告别过去，立足于在10维时空振动小弦。 Moreover, the theory easily swallows up Einsteins theory of gravity.此外，这个理论很容易吞了爱因斯坦的引力理论。 Witten has said, “Unlike conventional quantum field theory, string theory requires gravity.威滕说，与传统的量子场论“，弦理论需要的严重性。 I regard this fact as one of the greatest in- sights in science ever made.” But until recently, there has been a glaring weak spot: string theorists have been unable to probe all solutions of the model, failing miserably to examine what is called the “non-perturbative region,” which I will describe shortly.我认为这是最伟大的之一，在科学的景点做过的事实。“但直到最近，出现了一个明显的弱点：弦理论已经无法探测到了此模型的所有解决方案，否则惨败，研究什么是所谓的“非微扰地区，”不久，我将描述。 This is vitally important, since ultimately our universe (with its wonderfully diverse collection of galaxies, stars, planets, sub- atomic particles, and even people) may lie in this “non-perturbative region.” Until this region can be probed, we dont know if string theory is a theory of everything or a theory of nothing!这是非常重要的，因为最终我们的宇宙（其美妙收集来自不同的星系，恒星，行星，亚原子粒子，甚至人）可能在于这个“非微扰地区。直到这个地区”可以探讨，我们不知道弦理论是一切的理论 - 或有什么理论！ Thats what todays excitement is all about.这就是今天的激动是一回事。 For the first time, using a powerful tool called “duality,” physicists are now probing beyond just the tail, and finally seeing the outlines of a huge, unexpectedly beautiful lion at the other end.这是第一次，使用一个强大的工具，称为“双重性”，物理学家现在探测并不仅止于尾巴，终于看到了一个巨大的，美丽的狮子竟然在另一端的大纲。 Not knowing what to call it, Witten has dubbed it “M-theory.” In one stroke, M-theory has solved many of the embarrassing features of the theory, such as why we have 5 superstring theories.不知道该怎么称呼它，威滕把它称为“M理论。”弹指一挥间，M理论已经解决了诸如为什么我们有5个超弦理论的理论的，尴尬的许多功能。 Ultimately, it may solve the nagging question of where strings come from.最终，它可能解决了在字符串来自挥之不去的问题。 “Pea Brains” and the Mother of all Strings “豌豆大脑”和母亲的所有字符串 Einstein once asked himself if God had any choice in making the universe.爱因斯坦曾问自己，如果上帝在宇宙中作出任何选择。 Perhaps not, so it was embarrassing for string theorists to have five different self-consistent strings, all of which can unite the two fundamental theories in physics, the theory of gravity and the quantum theory.也许没有，所以它是弦理论家的尴尬有五种不同的自我一致的字符串，所有这些都可以团结的两个基本物理理论，引力理论和量子理论。 Each of these string theories looks completely different from the others.这些弦理论看起来完全从每个人不同。 They are based on different symmetries, with exotic names like E(8)xE(8) and O(32).它们是基于不同的对称性，如异国情调的名称（8）XE版（8）和O（32）。 Not only this, but superstrings are in some sense not unique: there are other non-string theories which contain “super- symmetry,” the key mathematical symmetry underlying superstrings.不仅如此，而且在某种意义上不超弦独特的是：有其他非字符串理论包含“超对称”的重要基础数学对称超弦。 (Changing light into electrons and then into gravity is one of the rather astonishing tricks performed by supersymmetry, which is the symmetry which can exchange particles with half-integral spin, like electrons and quarks, with particles of integral spin, like photons, gravitons, and W-particles. （改变光线进入到电子和严重性，然后是由超对称，这是可以交换对称半整数自旋粒子如电子和夸克，表现相当惊人的技巧之一，其整数自旋粒子，如光子，引力子，和W粒子。 In 11 dimensions, in fact, there are alternate super theories based on membranes as well as point particles (called super- gravity).在11个方面，事实上，上有膜，以及所谓的超微粒重力点（根据候补超级理论）。 In lower dimensions, there is moreover a whole zoo of super theories based on membranes in different dimensions.在较低的层面，而且有一个整体的超级理论动物园膜对不同尺寸的基础。 (For example, point particles are 0-branes, strings are 1-branes, membranes are 2-branes, and so on.) For the p-dimensional case, some wag dubbed them p-branes (pronounced “pea brains”). （例如，指向粒子0 -布拉涅斯，字符串是1布拉涅斯，膜为2布拉涅斯，等等。对于p维的情况），其中一些被称为摇摆的P -布拉涅斯（发音为“豌豆大脑”）。 But because p-branes are horribly difficult to work with, they were long considered just a historical curiosity, a trail that led to a dead-end.但是，因为P -布拉涅斯是可怕的困难工作，他们被认为只是一个长期的历史的好奇心，一个线索，导致一条死胡同。 (Michael Duff, in fact, has collected a whole list of unflattering comments made by referees to his National Science Foundation grant concerning his work on p- branes. One of the more charitable comments from a referee was: “He has a skewed view of the relative importance of various concepts in modern theoretical physics.”) So that was the mystery. （迈克尔达夫，事实上，已收集了由裁判向他的国家科学基金会直言不讳的评论有关他整批名单上的P -布拉涅斯工作。裁判从一更慈善意见之一是：“他有一个扭曲的看法在现代理论物理学的各种概念的相对重要性。“），所以这是个谜。 Why should supersymmetry allow for 5 superstrings and this peculiar, motley collection of p-branes?为什么要允许超5超弦和这一特殊的P -布拉涅斯五花八门？ Now we realize that strings, supergravity, and p-branes are just different aspects of the same theory.现在我们认识到，字符串，超引力，和P -布拉涅斯都是同样的理论只是不同方面。 M-theory (M for “membrane” or the “mother of all strings,” take your pick) unites the 5 superstrings into one theory and includes the p-branes as well. M理论的“膜”或所有字符串之母“，”以你的选择）（男凝聚成一个超弦理论，其中包括5名P -布拉涅斯以及。 To see how this all fits together, let us update the famous parable of the blind wise men and the elephant.要看到这一切组合在一起，让我们更新盲人智者和大象著名寓言。 Think of the blind men on the trail of the lion.想想对狮径瞎子。 Hearing it race by, they chase after it and desperately grab onto its tail (a one-brane).听证会是由种族，他们拼命地追逐它，抓住它的尾巴上（一膜的）。 Hanging onto the tail for dear life, they feel its one- dimensional form and loudly proclaim “Its a string!到尾巴死死抓住不放，他们认为它的一维形式，大声说：“这是一个字符串！ Its a string!”这是一个字符串！“ But then one blind man goes beyond the tail and grabs onto the ear of the lion.但是，人们又瞎子超越了尾巴，走上了狮子的耳朵争夺。 Feeling a two-dimensional surface (a membrane), the blind man proclaims, “No, its really a two-brane!” Then another blind man is able to grab onto the leg of the lion.感觉一个二维表面（1膜），盲人男子宣称：“不，这实在是一种双膜的！”接着另一个盲人能够抓住走上狮子腿。 Sensing a three-dimensional solid, he shouts, “No, youre both wrong.传感一个三维实体，他大喊一声“不，你俩都是错误的。 Its really a three-brane!” Actually, they are all right.这实在是一种三膜的！“其实，他们都是正确的。 Just as the tail, ear, and leg are different parts of the same lion, the string and various p- branes appear to be different limits of the same theory: M- theory.正如尾巴，耳朵，腿都是同一狮子，绳子，不同p -布拉涅斯不同地区不同的限制似乎是同样在这一理论：M理论。 Paul Townsend of Cambridge University, one of the architects of this idea, calls it “p-brane democracy,” ie all p- branes (including strings) are created equal.保罗汤森剑桥大学，本思想的设计师之一，称之为的“P -膜的民主”，即所有P -布拉涅斯（包括字符串）是一样的。 Schwarz puts a slightly different spin on this.施瓦茨把这个略有不同自旋。 He says, “we are in an Orwellian situation: all p-branes are equal, but some (namely strings) are more equal than others.他说，“我们正处在一个奥威尔的情况：所有P -布拉涅斯都是平等的，但一些国家（即字符串）比其他人平等的。 The point is that they are the only ones on which we can base a perturbation theory.” To understand unfamiliar concepts such as duality, perturbation theory, non-perturbative solutions, it is instructive to see where these concepts first entered into physics.问题是，他们是唯一的基础上，我们可以一个摄动理论。“了解陌生的概念，如对偶，摄动理论，非微扰的解决方案，它具有指导性，以了解这些概念第一次进入到物理。 Dualty Dualty The key tool to understanding this breakthrough is something “duality.” Loosely speaking, two theories are “dual” to each other if they can be shown to be equivalent under a certain interchange.关键工具来理解这一突破是什么“的两重性。”宽松地讲，这两种理论是“双重”对方如果能证明是根据一定的交换当量。 The simplest example of duality is reversing the role of electricity and magnetism in the equations discovered by James Clerk Maxwell of Cambridge University 130 years ago.对偶最简单的例子是扭转了电和磁的詹姆斯克拉克麦克斯韦剑桥大学发现130年前的方程的作用。 These are the equations which govern light, TV, X-rays, radar, dynamos, motors, transformers, even the Internet and computers.这些方程支配光，电视，X射线，雷达，发电机，电动机，变压器，即使是互联网和电脑。 The remarkable feature about these equations is that they remain the same if we interchange the magnetic B and electric fields E and also switch the electric charge e with the magnetic charge g of a magnetic “monopole”: E B and e g (In fact, the product eg is a constant.) This has important implications.关于这些方程的显着特征是，它们仍然是相同的，如果我们交换磁场B和电场E和还切换电荷与磁磁“单极”克费：电子 B和E 克（事实上，产品例如是一个常数。）这具有重要意义。 Often, when a theory cannot be solved exactly, we use an approximation scheme.通常，当一个理论不能完全解决，我们使用近似计划。 In first year calculus, for example, we recall that we can approximate certain functions by Taylors expansion.在第一年的微积分，例如，我们记得，我们可以近似由泰勒的扩张的某些职能。 Similarly, since e2 = 1/137 in certain units and is hence a small number, we can always approximate the theory by power expanding in e2.同样，由于 2，某些单位= 1 / 137和是一个小数目，因此，我们总是可以通过扩大权力近似理论 2。 So we add contributions of order e2 + e4 + e6 etc. in solving for, say, the collision of two particles.因此，我们添加的贡献秩序 2 + 4 + 6等，解决了，也就是说，两个粒子碰撞。 Notice that each contribution is getting smaller and smaller, so we can in principle add them all up.请注意，每个原则的贡献越来越小，因此我们可以添加他们都放弃了。 This generalization of Taylors expansion is called “perturbation theory,” where we perturb the system with terms containing e2.泰勒的这一扩张的推广是所谓的“摄动理论”，其中含有我们扰动 2方面的制度。 For example, in archery, perturbation theory is how we aim our arrows.例如，在射箭，摄动理论是我们的目标是怎样的箭。 With every motion of our arms, our bow gets closer and closer to aligning with the bulls eye.) But now try expanding in g2.随着我们的每一个武器的议案，我们鞠躬得到密切与公牛的眼睛对准。）但是现在试图在G 2扩大。 This is much tougher; in fact, if we expand in g2, which is large, then the sum g2 + g4 + g6 etc. blows up and becomes meaningless.这是非常强硬，事实上，如果我们扩大在G 2，大，那么总和克 2 +克+克 4 6等的冲击和变得毫无意义。 This is the reason why the “non-perturbative” region is so difficult to probe, since the theory simply blows up if we try to naively use perturbation theory for large coupling constant g.这就是为什么“非微扰”地区是如此难以探测的理论简单地打击，因为如果我们尝试了天真地使用大耦合常数湾摄动理论， So at first it appears hopeless that we could ever penetrate into the non-perturbative region.所以刚开始时似乎永远没有希望，我们可以渗透到非微扰地区。 (For example, if every motion of our arms got bigger and bigger, we would never be able to zero in and hit the target with the arrow.) But notice that because of duality, a theory of small e (which is easily solved) is identical to a theory of large g (which is difficult to solve). （例如，如果我们每一个武器的议案得到了越来越大，我们将永远不能为零，撞上同方向的目标。）但是请注意，由于对偶，一小（这是很容易解决的理论）是相同的一大克（这是很难解决理论）。 But since they are the same theory, we can use duality to solve for the non-perturbative region.但因为他们是同样的理论，我们可以使用双重性，解决了非微扰地区。 S, T, and U Dualty秒，T和U Dualty The first inkling that duality might apply in string theory was discovered by K. Kikkawa and M. Yamasaki of Osaka Univ.第一个暗示是在弦理论的双重性可能是由K.吉川申请和M.大阪大学山崎发现。 in 1984.于1984年。 They showed that if you “curled up” one of the extra dimensions into a circle with radius R, the theory was the same if we curled up this dimension with radius 1/R.他们发现，如果你“蜷缩”的额外维度一成一个半径为R的圆，这个理论是相同的，如果我们蜷缩这个层面半径为1 /河 This is now called T- duality: R 1/R When applied to various superstrings, one could reduce 5 of the string theories down to 3 (see figure).这就是现在所谓的T -对偶：遥控 1 /住宅时，适用于各种超弦，一可以减少字符串的理论到3 5（见附图）。 In 9 dimensions (with one dimension curled up) the Type IIa and IIb strings were identical, as were the E(8)xE(8) and O(32) strings.在9尺寸与一维（卷曲）类型及第字符串是一样的，因为人的E（8）XE版（8）和O（32）字符串。 Unfortunately, T duality was still a perturbative duality.不幸的是，两重性仍然是微扰两重性。 The next breakthrough came when it was shown that there was a second class of dualities, called S duality, which provided a duality between the perturbative and non-perturbative regions of string theory.下一个突破出现时，结果表明，有一个对偶的第二类，称为两重性，它提供了一个与弦理论的微扰和非微扰地区的两重性。 Another duality, called U duality, was even more powerful.另一个对偶，叫做U对偶，甚至更加强大。 Then Nathan Seiberg and Witten brilliantly showed how another form of duality could solve for the non-perturbative region in four dimensional supersymmetric theories.拿单Seiberg和威滕出色表现又如何对偶形式可以解决在四维超对称理论的非微扰地区。 However, what finally convinced many physicists of the power of this technique was the work of Paul Townsend and Edward Wit- ten.不过，终于说服了该技术的权力，是许多物理学家保罗汤森和爱德华威特- 10的工作。 They caught everyone by surprise by showing that there was a duality between 10 dimensional Type IIa strings and 11 dimension- al supergravity!他们措手不及通过展示，有一间10对偶维IIA型弦和11尺寸铝超引力大家！ The non-perturbative region of Type IIa strings, which was previously a forbidden region, was revealed to be governed by 11 dimensional supergravity theory, with one dimension curled up.作者：IIA型弦，原先是禁止区域的非微扰区，是由11日透露，维超引力理论与一维管，卷曲起来。 At this point, I remember that many physicists (myself included) were rubbing our eyes, not believing what we were seeing.在这一点上，我记得（包括我自己在内）的揉眼睛，不相信我们看到了许多物理学家。 I remember saying to myself, “But thats impossible!”我记得对自己说，“但是这是不可能的！” All of a sudden, we realized that perhaps the real “home” of string theory was not 10 dimensions, but possibly 11, and that the theory wasnt fundamentally a string theory at all!突然间，我们意识到，也许是真正的“家弦论”是不是10的尺寸，但可能增加到11人，没有根本的理论是在所有弦理论！ This revived tremendous interest in 11 dimensional theories and p- branes.这11维理论恢复和P -布拉涅斯极大兴趣。 Lurking in the 11th dimension was an entirely new theory which could reduce down to 11 dimensional supergravity as