量子临界态下的膜
Membranes at Quantum Criticality
摘要：
我们提出了一个量子膜理论，该理论的设计使得具有紧凑空间拓扑结构的膜的基态波函数再现了世界面上玻色弦的配分函数。该构造涉及处于量子临界状态的世界体积物质，在最简单的情况下由动力学临界指数z=2的Lifshitz标量描述。这个物质系统必须与一个新的世界体积引力理论相耦合，这个理论也表现出z=2的量子临界性。我们首先在D+1维时空中构造z=2的非相对论性“Lifshitz点引力”，然后专门研究适合于膜世界体积的D=2的临界情况。我们还表明，在第二个量子化的框架中，弦的配分函数再现，如果时空基态采取的形式的玻色-爱因斯坦凝聚体的膜在其第一个量子化的基态，相关的所有属。
英文摘要：
We propose a quantum theory of membranes designed such that the ground-state wavefunction of the membrane with compact spatial topology Σ_h reproduces the partition function of the bosonic string on worldsheet Σ_h. The construction involves worldvolume matter at quantum criticality, described in the simplest case by Lifshitz scalars with dynamical critical exponent z=2. This matter system must be coupled to a novel theory of worldvolume gravity, also exhibiting quantum criticality with z=2. We first construct such a nonrelativistic "gravity at a Lifshitz point" with z=2 in D+1 spacetime dimensions, and then specialize to the critical case of D=2 suitable for the membrane worldvolume. We also show that in the second-quantized framework, the string partition function is reproduced if the spacetime ground state takes the form of a Bose-Einstein condensate of membranes in their first-quantized ground states, correlated across all genera.
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