arXiv 1409.44172014-09hep-th

Spin Matrix Theory：AdS/CFT correspondence的量子力学模型

Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence

Troels Harmark, Marta Orselli

备注：: 36 pages, 3 figures. v2: Refs. added
DOI：: 10.1007/JHEP11(2014)134

摘要：

我们介绍了一种新的量子力学理论，称为自旋矩阵理论（SMT）。该理论与单个耦合常数g相互作用，并且基于谐振子的希尔伯特空间，该谐振子具有在李（超）代数表示中取值的自旋指数以及U（N）的伴随表示的矩阵指数。我们表明，SMT描述N=4的超杨米尔斯理论（SYM）的巨正则相图中的零温临界点附近。等价地，SMT产生于N=4 SYM的非相对论极限。尽管SMT是一个非相对论性的量子力学理论，但它包含了各种模仿AdS/CFT对应的相。此外，SMT的无限g极限可以映射到AdS_5 × S^5上的弦论的超对称扇区。我们详细研究了SU（2）SMT。在大N和低温下，它是一种自旋链理论，对于小g类似于平面规范理论，对于大g类似于非相对论性弦论。当升高温度时，由于有限N效应，发生部分解除禁闭转变。在足够高的温度下，部分退精细相具有经典的状态。我们发现，在任何耦合g的矩阵模型描述这一制度。当g=0时，它是一个有N^2+1个谐振子的理论，而当g较大时，它变成了2N个谐振子。

英文摘要：

We introduce a new quantum mechanical theory called Spin Matrix theory (SMT). The theory is interacting with a single coupling constant g and is based on a Hilbert space of harmonic oscillators with a spin index taking values in a Lie (super)algebra representation as well as matrix indices for the adjoint representation of U(N). We show that SMT describes N=4 super-Yang-Mills theory (SYM) near zero-temperature critical points in the grand canonical phase diagram. Equivalently, SMT arises from non-relativistic limits of N=4 SYM. Even though SMT is a non-relativistic quantum mechanical theory it contains a variety of phases mimicking the AdS/CFT correspondence. Moreover, the infinite g limit of SMT can be mapped to the supersymmetric sector of string theory on AdS_5 x S^5. We study SU(2) SMT in detail. At large N and low temperatures it is a theory of spin chains that for small g resembles planar gauge theory and for large g a non-relativistic string theory. When raising the temperature a partial deconfinement transition occurs due to finite-N effects. For sufficiently high temperatures the partially deconfined phase has a classical regime. We find a matrix model description of this regime at any coupling g. Setting g=0 it is a theory of N^2+1 harmonic oscillators while for large g it becomes 2N harmonic oscillators.

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