arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1106.4501hep-thcond-mat.str-elgr-qchep-phnucl-th
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从不动点到第五维

From Fixed Points to the Fifth Dimension

Raman Sundrum

摘要:

从共形流代数“几何化”的观点出发,将4D洛伦兹共形场论(CFT)映射到5D反de Sitter时空(AdS).一个大的N扩展的CFT导致(无限多)弱耦合的AdS粒子,在一对一的对应关系与最小的颜色单重CFT主要运营商。如果所有,但有限数量的“保护”的主要运营商有非常大的标度尺寸,它表明,存在一个低AdS曲率有效场论制度相应的有限集的AdS粒子。有效的5D规范理论和广义相对论在AdS上是以这种方式从受保护的CFT原色、全局对称性的Noether电流和能量动量张量的最稳健的例子中导出的。Witten的处方计算CFT本地运营商的AdS对偶内的。主要的新贡献是AdS耦合的5D局部性的推导。这是通过研究一个封闭的IR变形的CFT在大N“平面”近似,其中的离散谱和存在的S-矩阵允许的约束的么正性和交叉对称性来解决(在标准的方式)的树级扩展的4D本地“胶球”耦合。当变形被小心地删除,这个4D局部性(与合理的技术假设指定其精确的性质)与恢复的共形对称性相结合,产生5D AdS局部性。在这个意义上,AdS/CFT对偶性说明了涌现相对论的可能性,以及强耦合的特殊作用,简要讨论。小心采取结束与定义良好的数学表达式和收敛积分的每一步。

英文摘要:

4D Lorentzian conformal field theory (CFT) is mapped into 5D anti-de Sitter spacetime (AdS), from the viewpoint of "geometrizing" conformal current algebra. A large-N expansion of the CFT is shown to lead to (infinitely many) weakly coupled AdS particles, in one-to-one correspondence with minimal-color-singlet CFT primary operators. If all but a finite number of "protected" primary operators have very large scaling dimensions, it is shown that there exists a low-AdS-curvature effective field theory regime for the corresponding finite set of AdS particles. Effective 5D gauge theory and General Relativity on AdS are derived in this way from the most robust examples of protected CFT primaries, Noether currents of global symmetries and the energy-momentum tensor. Witten's prescription for computing CFT local operator correlators within the AdS dual is derived. The main new contribution is the derivation of 5D locality of AdS couplings. This is accomplished by studying a confining IR-deformation of the CFT in the large-N "planar" approximation, where the discrete spectrum and existence of an S-matrix allow the constraints of unitarity and crossing symmetry to be solved (in standard fashion) by a tree-level expansion in terms of 4D local "glueball" couplings. When the deformation is carefully removed, this 4D locality (with plausible technical assumptions specifying its precise nature) combines with the restored conformal symmetry to yield 5D AdS locality. The sense in which AdS/CFT duality illustrates the possibility of emergent relativity, and the special role of strong coupling, are briefly discussed. Care is taken to conclude each step with well-defined mathematical expressions and convergent integrals.

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