黑洞物理一个新前沿蔡荣根

1、黑洞物理: 一个新前沿,蔡荣根 中科院理论物理研究所,* 引力是自然界四种基本相互作用力之一。 （其它三种：电磁作用，强相互作用和弱相互作用）,* 从牛顿的万有引力定律到爱因斯坦的广义相对论 问题： （1）广义相对论成立从亚毫米到太阳系尺度 （2）广义相对论是经典理论，引力的量子性质如何？,引力理论 a bet established in 1997,从黑洞热力学，我们学到的重要一课：,E,S,M,S,V,A,V,A,SV,SA,普通的热力学体系,黑洞,Black hole is a window to quantum gravity,Thermodynamics of black hole：

2、,（S.Hawking, 1974, J. Bekenstein, 1973),在表面面积为A的引力体系中，SA/4G,(t Hooft, 1993),(L. Susskind, 1994),引力的全息性质（Holography)：,引力体系的自由度就象分布在这一体系的 表面上一样。或者说人们可以用这一引力 体系的表面自由度来描述整个引力体系。,一个D维包含引力的理论=一个（D-1)维不包含引力的理论,(C. Vafa),(A. Strminger),事情的另一方面是关于黑洞熵的统计自由度！,（String Theory, 1996),In Loop Quantum Gravity,(A.As

3、htekar,J.Baez,A. Corichi and K. Krannov, PRL,1998),全息原理在弦论中的实现(1997)：,（J. Maldacena),在反德西特时空（带一个紧致空间）上的 超弦理论（或M理论）等价（对偶）于在 这个反德西特时空边界上的一个共形场论。,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 对偶性字典 :,这里 有二个解释: 在引力这边: 这些对应在AdS bulk中传播的场的边界值。 在AdS边界上场论这一边: 这些场相应于边界共形场论许多算符耦合的外源。,AdS/CFT, 证据如何？,（1）整体对称性: AdS_5 X S5 N=4 SYM （2）关联函数的计算,AdS/CFT Conj

5、ecture： 理论价值？ 应用价值？ 强耦合系统,QCD,高温超导,QCD 相图：,如何从AdS/CFT来理解低能QCD的性质？ (1) top-down (从上到下） (2) bottom-up （从下往上）,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 (全息超导）,1950, Landau-Ginzburg theory,1957, BCS theory: interactions with phonons,超导现象： 电阻消失 (H. Onnes, 1911) Meissner effect (1933),1980s: 高温超导， 2000s: 铁基超导,2) AdS/CMT,如何实现一个全息超导模型？,CFT AdS/CFT 引力 整体对称性 阿贝尔规范场 标量算符 标量场 温度 黑洞 相变 高温/无毛；低温/有毛,

7、Building a holographic superconductor S. Hartnoll, C.P. Herzog and G. Horowitz, arXiv: 0803.3295 PRL 101, 031601 (2008),高温相（无毛黑洞):,一个普适的能隙（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）引力理论和流体力学的关系,Black holes: The Membrane Paradigm, 1986 Gravity and Hydrodynamics: Lectures on the fluid-gravity correspondence M. Rangamani, Class. Quant. Grav. 26: 224003, 2009,引力与热力学和流体力学一样，具有相当的普适性,研究这两者的关系 利用非平衡

10、流体力学来研究动力学时空的性质 动力学黑洞的热力学性质，应用于QGP 利用引力理论来研究流体力学中的问题如激波，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 和七个千禧年问题,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