1、黑洞物理: 一個(gè)新前沿,蔡榮根 中科院理論物理研究所,* 引力是自然界四種基本相互作用力之一。 （其它三種：電磁作用，強(qiáng)相互作用和弱相互作用）,* 從牛頓的萬(wàn)有引力定律到愛因斯坦的廣義相對(duì)論 問(wèn)題： （1）廣義相對(duì)論成立從亞毫米到太陽(yáng)系尺度 （2）廣義相對(duì)論是經(jīng)典理論，引力的量子性質(zhì)如何？,引力理論 a bet established in 1997,從黑洞熱力學(xué)，我們學(xué)到的重要一課：,E,S,M,S,V,A,V,A,SV,SA,普通的熱力學(xué)體系,黑洞,Black hole is a window to quantum gravity,Thermodynamics of black hole：

2、,（S.Hawking, 1974, J. Bekenstein, 1973),在表面面積為A的引力體系中，SA/4G,(t Hooft, 1993),(L. Susskind, 1994),引力的全息性質(zhì)（Holography)：,引力體系的自由度就象分布在這一體系的 表面上一樣。或者說(shuō)人們可以用這一引力 體系的表面自由度來(lái)描述整個(gè)引力體系。,一個(gè)D維包含引力的理論=一個(gè)（D-1)維不包含引力的理論,(C. Vafa),(A. Strminger),事情的另一方面是關(guān)于黑洞熵的統(tǒng)計(jì)自由度！,（String Theory, 1996),In Loop Quantum Gravity,(A.As

3、htekar,J.Baez,A. Corichi and K. Krannov, PRL,1998),全息原理在弦論中的實(shí)現(xiàn)(1997)：,（J. Maldacena),在反德西特時(shí)空（帶一個(gè)緊致空間）上的 超弦理論（或M理論）等價(jià)（對(duì)偶）于在 這個(gè)反德西特時(shí)空邊界上的一個(gè)共形場(chǎng)論。,典型例子：,IIB superstring theory on AdS5 x S5 N=4 SYM Theory,(E. Witten),(A. Polyakov),(I. Klebanov),(S. Gubser),AdS/CFT correspondence (J. Maldacena, 1997),“Rea

4、l conceptual change in our thinking about Gravity.” (E. Witten, Science 285 (1999) 512),IIB superstring theory on AdS5 x S5 N=4 SYM Theory,AdS/CFT 對(duì)偶性字典 :,這里 有二個(gè)解釋: 在引力這邊: 這些對(duì)應(yīng)在AdS bulk中傳播的場(chǎng)的邊界值。 在AdS邊界上場(chǎng)論這一邊: 這些場(chǎng)相應(yīng)于邊界共形場(chǎng)論許多算符耦合的外源。,AdS/CFT, 證據(jù)如何？,（1）整體對(duì)稱性: AdS_5 X S5 N=4 SYM （2）關(guān)聯(lián)函數(shù)的計(jì)算,AdS/CFT Conj

5、ecture： 理論價(jià)值？ 應(yīng)用價(jià)值？ 強(qiáng)耦合系統(tǒng),QCD,高溫超導(dǎo),QCD 相圖：,如何從AdS/CFT來(lái)理解低能QCD的性質(zhì)？ (1) top-down (從上到下） (2) bottom-up （從下往上）,1) AdS/QCD,RHICs heavy Ion Collision,PRL98, 172301(2007), nucl-ex/0611018 PRL99, 172301(2007), nucl-ex/0706.1522,RHIC:,AdS/CFT:,Kovtun, Son and Starinet, PRL (05),（Cai et al, 2008, 2009, 2010),

6、(Brigante et al, PRL 2008),Holographic superconductor models (全息超導(dǎo)）,1950, Landau-Ginzburg theory,1957, BCS theory: interactions with phonons,超導(dǎo)現(xiàn)象： 電阻消失 (H. Onnes, 1911) Meissner effect (1933),1980s: 高溫超導(dǎo)， 2000s: 鐵基超導(dǎo),2) AdS/CMT,如何實(shí)現(xiàn)一個(gè)全息超導(dǎo)模型？,CFT AdS/CFT 引力 整體對(duì)稱性 阿貝爾規(guī)范場(chǎng) 標(biāo)量算符 標(biāo)量場(chǎng) 溫度 黑洞 相變 高溫/無(wú)毛；低溫/有毛,

7、Building a holographic superconductor S. Hartnoll, C.P. Herzog and G. Horowitz, arXiv: 0803.3295 PRL 101, 031601 (2008),高溫相（無(wú)毛黑洞):,一個(gè)普適的能隙（gap): 10%,BCS theory: 3.5 K. Gomes et al, Nature 447, 569 (2007),3) Holographic optics and negative refractive index A. Amariti et al., arXiv: 1006.5714,The free

8、 propagation of light in curved spacetime The propagation of light inside a material in flat space,Metamaterials: cloaking devices, perfect lenses, photonic black holes,Some with negative refractive index (left-handed materials),V.G. Veselago, Sov. Phys. Usp 10, 509 (1968) R.A. Shelby et al., Scienc

9、e 292, 77 (2001),Einsteins Field Equations:,Incompressible Navier-Stokes Equations:,4）引力理論和流體力學(xué)的關(guān)系,Black holes: The Membrane Paradigm, 1986 Gravity and Hydrodynamics: Lectures on the fluid-gravity correspondence M. Rangamani, Class. Quant. Grav. 26: 224003, 2009,引力與熱力學(xué)和流體力學(xué)一樣，具有相當(dāng)?shù)钠者m性,研究這兩者的關(guān)系 利用非平衡

10、流體力學(xué)來(lái)研究動(dòng)力學(xué)時(shí)空的性質(zhì) 動(dòng)力學(xué)黑洞的熱力學(xué)性質(zhì)，應(yīng)用于QGP 利用引力理論來(lái)研究流體力學(xué)中的問(wèn)題如激波，湍流 ,Clay Mathematics Institute (/millennium) The seven Millennium Prize Problems (US$7 million):,Birch and Swinnerton-Dyer Conjecture 2) Hodge Conjecture 3) Navier-Stokes equations 4) P vs NP 5) Poincare Conjecture 6) Riem

11、ann Hypothesis 7) Yang-Mills theory,AdS/CFT 和七個(gè)千禧年問(wèn)題,Waves follow our boat as we meander across the lake, and turbulent air currents follow our flight in a modern jet. Mathematicians and physicists believe that an explanation for and the prediction of both the breeze and the turbulence can be found

12、through an understanding of solutions to the Navier-Stokes equations. Although these equations were written down in the 19th Century, our understanding of them remains minimal. The challenge is to make substantial progress toward a mathematical theory which will unlock the secrets hidden in the Navi

13、er-Stokes equations.,Navier-Stokes Equation:,The laws of quantum physics stand to the world of elementary particles in the way that Newtons laws of classical mechanics stand to the macroscopic world. Almost half a century ago, Yang and Mills introduced a remarkable new framework to describe elementa

14、ry particles using structures that also occur in geometry. Quantum Yang-Mills theory is now the foundation of most of elementary particle theory, and its predictions have been tested at many experimental laboratories, but its mathematical foundation is still unclear. The successful use of Yang-Mills

15、 theory to describe the strong interactions of elementary particles depends on a subtle quantum mechanical property called the mass gap: the quantum particles have positive masses, even though the classical waves travel at the speed of light. This property has been discovered by physicists from experiment and confirmed by computer simulations, but it still has not been underst