作者:
Schwinger (千金之子不死於盜賊)
2015-04-30 23:46:50我稍微解釋一下AdS/CFT的對偶和全息原理一些故事好了,純嘴砲
所謂的AdS就是anti-de Sitter空間,這個空間會被發現是來自於愛因斯坦的宇宙常數
以前的人只知道狹義相對論的4維Minkowski空間,但是這空間是完全平坦的,自從愛因斯坦
的廣義相對論1916年橫空出世之後,人類才知道時空是彎曲的,而且我們可以證明描述
廣義相對論球對稱宇宙有一個非常重要的度規(FLRW metric) 以前我從課本只知道FRW
三個而已,這表示這些人真的很厲害,愛因斯坦的東西出來就一堆人來做了
Friedmann–Lemaître–Robertson–Walker metric
http://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertso
n%E2%80%93Walker_metric
當時1924年有一個優秀蘇聯物理學家Alexander Friedmann(就是上面那個F)
幫愛因斯坦做了數學和物理解釋,當時他的結論是廣義相對論告訴我們宇宙是會膨脹的
http://en.wikipedia.org/wiki/Alexander_Friedmann
http://en.wikipedia.org/wiki/Friedmann_equations
但是愛因斯坦出自於當時所有哲學上的思考就馬上打槍這個蘇聯物理學家的想法,
當時為了讓愛因斯坦場方程是靜態的,他弄一個宇宙常數,後來愛因斯坦當時在哈伯天文台
就發現宇宙是膨脹的,愛因斯坦宇宙常數確變成宇宙學意外非常重要的東西,而且物理學家
也發現FRLW度規在宇宙學對應數學幾何有三種K=0 K=1 K=-1,分別是Minkowski空間,
de Sitter和anti-de Sitter空間,而Willem de Sitter也是一個荷蘭著名的天文學家
事實上負曲率是一個非常漂亮的數學也被大數學家Poincaré和藝術家研究的很深入
Poincaré disk model,這個幾何有一種非常漂亮的性質就是保角的特性(conformal)
http://en.wikipedia.org/wiki/Poincar%C3%A9_disk_model
至於CFT就是高維的保角性質,坦白說CFT(conformal field theory)我不是很熟
只知道是1984年三個物理學家Polyakov,Belavin和Zamolodchikov提出來的,經過一堆超級
無敵變態的數學家Moore,Seiberg,Verlinde,Witten在1988年這理論基本上已經被做到天上去了
至於CFT的延伸像是頂點算子代數和一堆代數甚至裡面的模不變性,最有名的是Kac-Moody
代數和Richard Borcherds著名的費爾茲獎工作 月光猜想(很浪漫吧)
http://w3.math.sinica.edu.tw/math_media/d354/35403.pdf
言歸正傳全息原理就是黑洞所有訊息可以從其表面的用量子場論的方式得到
怎麼得到呢? 答案是用AdS/CFT對偶得到,而且他有一些令人驚訝的性質
http://en.wikipedia.org/wiki/AdS/CFT_correspondence
AdS/CFT對偶最有名的例子，就是AdS_5\times S^5積空間上的IIB型弦理論是相等於四維
邊界上的N=4超對稱楊-Mills理論
說AdS/CFT是弦論的第三次革命也不為過,這是當時1997年一個哈佛大學
還沒拿到終身職的教授阿根廷裔的Juan Maldacena所做的一個猜想,
但是當時沒有人相信就是了,因為這個直覺有點怪,宇宙的表面竟然是負曲率的
anti-de Sitter空間,然後當時人們(我認為啦)最寄予厚望的是解決夸克的作用力,比如
夸克禁閉,高溫超導這種太強的力,因為利用AdS/CFT對偶可以知道,某些超強的力對偶就
變成超弱,這樣使得問題可解,但是我認識的凝態物理學家認為這個不太可靠,
甚至人類活著最偉大的凝態物理學家Philip Anderson和著名物理學家Larry McLerran
也給一個超中肯的評論
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
做這個的現在應該是找不到工作,不過可以學到一堆工具就是了,如果你有本事學起來很好
我想做真正做流體力學實際問題的一輩子應該也不會用到renormalization group和CFT吧