我稍微解释一下AdS/CFT的对偶和全息原理一些故事好了,纯嘴砲
所谓的AdS就是anti-de Sitter空间,这个空间会被发现是来自于爱因斯坦的宇宙常数
以前的人只知道狭义相对论的4维Minkowski空间,但是这空间是完全平坦的,自从爱因斯坦
的广义相对论1916年横空出世之后,人类才知道时空是弯曲的,而且我们可以证明描述
广义相对论球对称宇宙有一个非常重要的度规(FLRW metric) 以前我从课本只知道FRW
三个而已,这表示这些人真的很厉害,爱因斯坦的东西出来就一堆人来做了
Friedmann–Lemaître–Robertson–Walker metric
http://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertso
n%E2%80%93Walker_metric
当时1924年有一个优秀苏联物理学家Alexander Friedmann(就是上面那个F)
帮爱因斯坦做了数学和物理解释,当时他的结论是广义相对论告诉我们宇宙是会膨胀的
http://en.wikipedia.org/wiki/Alexander_Friedmann
http://en.wikipedia.org/wiki/Friedmann_equations
但是爱因斯坦出自于当时所有哲学上的思考就马上打枪这个苏联物理学家的想法,
当时为了让爱因斯坦场方程是静态的,他弄一个宇宙常数,后来爱因斯坦当时在哈伯天文台
就发现宇宙是膨胀的,爱因斯坦宇宙常数确变成宇宙学意外非常重要的东西,而且物理学家
也发现FRLW度规在宇宙学对应数学几何有三种K=0 K=1 K=-1,分别是Minkowski空间,
de Sitter和anti-de Sitter空间,而Willem de Sitter也是一个荷兰著名的天文学家
事实上负曲率是一个非常漂亮的数学也被大数学家Poincaré和艺术家研究的很深入
Poincaré disk model,这个几何有一种非常漂亮的性质就是保角的特性(conformal)
http://en.wikipedia.org/wiki/Poincar%C3%A9_disk_model
至于CFT就是高维的保角性质,坦白说CFT(conformal field theory)我不是很熟
只知道是1984年三个物理学家Polyakov,Belavin和Zamolodchikov提出来的,经过一堆超级
无敌变态的数学家Moore,Seiberg,Verlinde,Witten在1988年这理论基本上已经被做到天上去了
至于CFT的延伸像是顶点算子代数和一堆代数甚至里面的模不变性,最有名的是Kac-Moody
代数和Richard Borcherds著名的费尔兹奖工作 月光猜想(很浪漫吧)
http://w3.math.sinica.edu.tw/math_media/d354/35403.pdf
言归正传全息原理就是黑洞所有讯息可以从其表面的用量子场论的方式得到
怎么得到呢? 答案是用AdS/CFT对偶得到,而且他有一些令人惊讶的性质
http://en.wikipedia.org/wiki/AdS/CFT_correspondence
AdS/CFT对偶最有名的例子，就是AdS_5\times S^5积空间上的IIB型弦理论是相等于四维
边界上的N=4超对称杨-Mills理论
说AdS/CFT是弦论的第三次革命也不为过,这是当时1997年一个哈佛大学
还没拿到终身职的教授阿根廷裔的Juan Maldacena所做的一个猜想,
但是当时没有人相信就是了,因为这个直觉有点怪,宇宙的表面竟然是负曲率的
anti-de Sitter空间,然后当时人们(我认为啦)最寄予厚望的是解决夸克的作用力,比如
夸克禁闭,高温超导这种太强的力,因为利用AdS/CFT对偶可以知道,某些超强的力对偶就
变成超弱,这样使得问题可解,但是我认识的凝态物理学家认为这个不太可靠,
甚至人类活着最伟大的凝态物理学家Philip Anderson和著名物理学家Larry McLerran
也给一个超中肯的评论
http://en.wikipedia.org/wiki/AdS/CFT_correspondence
Criticism
With many physicists turning towards string-based methods to attack problems
in nuclear and condensed matter physics, some theorists working in these
areas have expressed doubts about whether the AdS/CFT correspondence can
provide the tools needed to realistically model real-world systems. In a talk
at the Quark Matter conference in 2006,[49] Larry McLerran pointed out that
the N=4 super Yang–Mills theory that appears in the AdS/CFT correspondence
differs significantly from quantum chromodynamics, making it difficult to
apply these methods to nuclear physics. According to McLerran,
N=4 supersymmetric Yang–Mills is not QCD ... It has no mass scale and is
conformally invariant. It has no confinement and no running coupling
constant. It is supersymmetric. It has no chiral symmetry breaking or mass
generation. It has six scalar and fermions in the adjoint representation ...
It may be possible to correct some or all of the above problems, or, for
various physical problems, some of the objections may not be relevant. As yet
there is not consensus nor compelling arguments for the conjectured fixes or
phenomena which would insure that the N=4 supersymmetric Yang Mills results
would reliably reflect QCD.[49]
In a letter to Physics Today, Nobel laureate Philip W. Anderson voiced
similar concerns about applications of AdS/CFT to condensed matter physics,
stating
As a very general problem with the AdS/CFT approach in condensed-matter
theory, we can point to those telltale initials "CFT"—conformal field
theory. Condensed-matter problems are, in general, neither relativistic nor
conformal. Near a quantum critical point, both time and space may be scaling,
but even there we still have a preferred coordinate system and, usually, a
lattice. There is some evidence of other linear-T phases to the left of the
strange metal about which they are welcome to speculate, but again in this
case the condensed-matter problem is overdetermined by experimental facts.[50]
八卦是
做这个的现在应该是找不到工作,不过可以学到一堆工具就是了,如果你有本事学起来很好
我想做真正做流体力学实际问题的一辈子应该也不会用到renormalization group和CFT吧