论文标题
全息相关功能在有限密度和/或有限温度下的功能
Holographic correlation functions at finite density and/or finite temperature
论文作者
论文摘要
我们以有限密度和/或有限温度计算标量运算符的一个和两点函数。在有限密度和零温度的情况下，我们认为只有标量运算符才能具有非零的VEV。在化学势和温度都是有限的情况下，我们在温度T的功率和化学势$ω$中提出了两点相关器的系统扩展。 全息结果与OPE的一般形式一致，该形式表明，两点函数可以作为Gegenbauer多项式的线性组合$ C_J^{（1）}（ξ）$，但与系数依赖于该系数，但现在取决于温度和化学电位，以及CFT数据。此扩展中的领先术语来自标量运算符$ ϕ^2 $的期望值，R-Current $ {\ Cal J}^μ__{ϕ_3} $和Energy-Momentum Tensor $ t^{μν} $。 通过使用R-Current的病房身份，并将两点相关器的全息结果的适当项与OPE中的相应项进行比较，我们得出了背景的R-Charge密度的值。与黑洞的热力学分析相结合的令人信服的一致性。最后，在有限温度的情况下，以及操作员的较大时间或空间距离的极限，我们确定了两点相关器的行为。
We calculate holographically one and two-point functions of scalar operators at finite density and/or finite temperature. In the case of finite density and zero temperature we argue that only scalar operators can have non-zero VEVs. In the case in which both the chemical potential and the temperature are finite, we present a systematic expansion of the two-point correlators in powers of the temperature T and the chemical potential $Ω$. The holographic result is in agreement with the general form of the OPE which dictates that the two-point function may be written as a linear combination of the Gegenbauer polynomials $C_J^{(1)}(ξ)$ but with the coefficients depending now on both the temperature and the chemical potential, as well as on the CFT data. The leading terms in this expansion originate from the expectation values of the scalar operator $ϕ^2$, the R-current ${\cal J}^μ_{ϕ_3}$ and the energy-momentum tensor $T^{μν}$. By employing the Ward identity for the R-current and by comparing the appropriate term of the holographic result for the two-point correlator to the corresponding term in the OPE, we derive the value of the R-charge density of the background. Compelling agreement with the analysis of the thermodynamics of the black hole is found. Finally, we determine the behaviour of the two-point correlators, in the case of finite temperature, and in the limit of large temporal or spatial distance of the operators.
