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arXiv 0704.2230hep-th
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AdS_2上的弦与非临界M理论的高能极限

Strings on AdS_2 and the High-Energy Limit of Noncritical M-Theory

Petr Horava, Cynthia A. Keeler

摘要:

2+1维非临界M理论被定义为二维平面上非相对论费米液体的双标度极限。在这里,我们在高能极限下研究这种非临界M-理论,类似于弦论的α' \to \infty极限。在相关的二维0A型弦的情况下,我们论证了共形的α' \to \infty极限导致了AdS_2,其传播费米子的质量由RR通量的值决定。在这里,我们提供的证据表明,在高能极限下,非临界M理论的自然基态类似地描述了AdS_2 \times S^1时空,它具有无质量的传播费米子。我们认为,在这种背景下的时空有效理论是由拓扑的高自旋扩展的共形陈-西蒙斯引力在2+1维,始终耦合到一个无质量的狄拉克场。有趣的是,最初的非相对论性费米子所占据的二维平面本质上是与AdS_2 \times S^1时空的对称群相关联的扭量空间;因此,至少在高能极限,非临界M理论可以非微扰地描述为“扭量空间上的费米液体”。"

英文摘要:

Noncritical M-theory in 2+1 dimensions has been defined as a double-scaling limit of a nonrelativistic Fermi liquid on a flat two-dimensional plane. Here we study this noncritical M-theory in the limit of high energies, analogous to the α'\to\infty limit of string theory. In the related case of two-dimensional Type 0A strings, it has been argued that the conformal α'\to\infty limit leads to AdS_2 with a propagating fermion whose mass is set by the value of the RR flux. Here we provide evidence that in the high-energy limit, the natural ground state of noncritical M-theory similarly describes the AdS_2\times S^1 spacetime, with a massless propagating fermion. We argue that the spacetime effective theory in this background is captured by a topological higher-spin extension of conformal Chern-Simons gravity in 2+1 dimensions, consistently coupled to a massless Dirac field. Intriguingly, the two-dimensional plane populated by the original nonrelativistic fermions is essentially the twistor space associated with the symmetry group of the AdS_2\times S^1 spacetime; thus, at least in the high-energy limit, noncritical M-theory can be nonperturbatively described as a "Fermi liquid on twistor space."

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