具有稳定共形因子的引力理论的调制基态
Modulated Ground State of Gravity Theories with Stabilized Conformal Factor
摘要：
讨论了共形约化$R+R^2$欧氏引力理论中高阶导数项对共形因子的稳定性。平坦时空对非零动量模式的凝聚是不稳定的，并且它们在高于$R^2$项的耦合$β$的临界值的调制相位中“凝聚”。通过采用变分，数值和晶格方法相结合，我们表明，在半经典极限相应的功能积分是由一个单一的非线性平面波频率$\approx 1/\sqrtβ \lp$为主。我们认为，该理论的基态的特点是在普朗克尺度的平移不变性的自发破缺。
英文摘要：
We discuss the stabilization of the conformal factor by higher derivative terms in a conformally reduced $R+R^2$ Euclidean gravity theory. The flat spacetime is unstable towards the condensation of modes with nonzero momentum, and they "condense" in a modulated phase above a critical value of the coupling $β$ of the $R^2$ term. By employing a combination of variational, numerical and lattice methods we show that in the semiclassical limit the corresponding functional integral is dominated by a single nonlinear plane wave of frequency $\approx 1/\sqrtβ \lp$. We argue that the ground state of the theory is characterized by a spontaneous breaking of translational invariance at Planckian scales.
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