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arXiv 0811.2217hep-thcond-mat.mes-hallcond-mat.str-elhep-ph
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量子临界性与杨-米尔斯规范理论

Quantum Criticality and Yang-Mills Gauge Theory

Petr Horava

摘要:

我们提出了一族D+1维的非相对论性Yang-Mills规范理论,其自由场极限具有无隙激发和动力学临界指数z=2的量子临界行为。基态波函数与D维相对论杨-米尔斯的配分函数密切相关。规范耦合在上临界时空维(等于4+1)中表现出对数标度和渐近自由。这些理论可以通过一个相关的算子在红外线中变形,该算子将庞加莱不变性恢复为偶然的对称性。在大N极限下,我们的非相对论性规范理论可以预期具有弱弯曲的引力场。

英文摘要:

We present a family of nonrelativistic Yang-Mills gauge theories in D+1 dimensions whose free-field limit exhibits quantum critical behavior with gapless excitations and dynamical critical exponent z=2. The ground state wavefunction is intimately related to the partition function of relativistic Yang-Mills in D dimensions. The gauge couplings exhibit logarithmic scaling and asymptotic freedom in the upper critical spacetime dimension, equal to 4+1. The theories can be deformed in the infrared by a relevant operator that restores Poincare invariance as an accidental symmetry. In the large-N limit, our nonrelativistic gauge theories can be expected to have weakly curved gravity duals.

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