论文标题

广告时空中的宇宙弦周围的有限温度电荷和当前密度与紧凑的尺寸

Finite temperature charge and current densities around a cosmic string in AdS spacetime with compact dimension

论文作者

de Mello, E. R. Bezerra, Santos, W. Oliveira dos, Saharian, A. A.

论文摘要

对于具有一般曲率耦合参数的庞大标量场,我们研究了对Hadamard函数的有限温度贡献,以及对磁性通量载有$(d+1)$(d+1)$(d+1)的磁性宇宙字符串的磁通量的几何形状和电流密度的贡献,并具有局部局部空间固定的空间空间调节。对于$ d = 4 $,在AD/CFT二元性的上下文中,ADS边界上的几何形状对应于沿其轴线压实的宇宙字符串作为线性缺陷。与Minkowski散装的情况相反,化学电位上的上限不取决于场质量,并且由紧凑型尺寸的长度和封闭的磁通量完全确定。唯一的非零组分对应于电荷密度,对应于方位角电流,沿紧凑型尺寸对应于电流。它们是磁通量的周期性功能,其周期等于通量量子。电荷密度是奇数功能,电流甚至是化学电位的功能。在高温下,重力场和拓扑对电荷密度的影响是亚尺寸的,并且在相应的膨胀中的主要项与Minkowski SpaceTime中的电荷密度相吻合。当前的密度是拓扑引起的数量,在高温下的行为与温度的线性依赖性完全不同。在较小的温度和小于临界值的化学电位下,对于庞大和无质量场的热期望值都被指数抑制。

For a massive scalar field with a general curvature coupling parameter, we investigate the finite temperature contributions to the Hadamard function and to the charge and current densities in the geometry of a magnetic flux carrying generalized cosmic string embedded in $(D+1)$-dimensional locally AdS spacetime with a compactified spatial dimension. For $D=4$, the geometry on the AdS boundary, in the context of the AdS/CFT duality, corresponds to a cosmic string as a linear defect, compactified along its axis. In contrast to the case of the Minkowski bulk, the upper bound on the chemical potential does not depend on the field mass and is completely determined by the length of compact dimension and by the enclosed magnetic flux. The only nonzero components correspond to the charge density, to the azimuthal current and to the current along the compact dimension. They are periodic functions of magnetic fluxes with the period equal to the flux quantum. The charge density is an odd function and the currents are even functions of the chemical potential. At high temperatures the influence of the gravitational field and topology on the charge density is subdominant and the leading term in the corresponding expansion coincides with that for the charge density in the Minkowski spacetime. The current densities are topology-induced quantities and their behavior at high temperatures is completely different with the linear dependence on the temperature. At small temperatures and for chemical potentials smaller than the critical value, the thermal expectation values are exponentially suppressed for both massive and massless fields.

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