Thermodynamic stability from Lorentzian path integrals and codimension-two singularities

IF 5.4 1区 物理与天体物理 Q1 Physics and Astronomy
Hong Zhe Vincent Chen
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引用次数: 0

Abstract

It has previously been shown how the gravitational thermal partition function can be obtained from a Lorentzian path integral. Unlike the Euclidean case, the integration contour over Lorentzian metrics is not immediately ruled out by the conformal factor problem. One can then ask whether this contour can be deformed to pick up nontrivial contributions from various saddle points. In Einstein-Maxwell theory, we argue that the relevance of each black hole saddle to the thermal partition function depends on its thermodynamic stability against variations in energy, angular momentum, and charge. The argument involves consideration of constrained saddles where area and quantities associated with angular momentum and charge are fixed on a codimension-two surface. Consequently, this surface possesses not only a conical singularity, but two other types of singularities. The latter are characterized by shifts along the surface and along the Maxwell gauge group acquired as one winds around near the surface in a metric-orthogonal and connection-horizontal manner. We first study this enlarged class of codimension-two singularities in generality and propose an action for singular configurations. We then incorporate these configurations into the path integral calculation of the partition function, focusing on three-dimensional spacetimes to simplify the treatment of angular momentum.

洛伦兹路径积分和余维二奇异的热力学稳定性
以前已经证明了如何从洛伦兹路径积分中得到引力热配分函数。与欧几里得情况不同,洛伦兹度量上的积分轮廓不会立即被保形因子问题所排除。然后,人们可以问这个轮廓是否可以变形,以从不同的鞍点拾取非平凡的贡献。在爱因斯坦-麦克斯韦理论中,我们认为每个黑洞鞍与热配分函数的相关性取决于其对能量、角动量和电荷变化的热力学稳定性。该论证涉及到约束鞍的考虑,其中与角动量和电荷相关的面积和数量固定在协维二曲面上。因此,这个曲面不仅具有圆锥奇点,而且具有另外两种奇点。后者的特征是沿着表面和麦克斯韦规范群的位移,这是在一个人以公制正交和连接水平的方式绕着表面旋转时获得的。我们首先从广义上研究了这类扩大的余维二奇点,并给出了奇异位形的作用。然后,我们将这些构型纳入配分函数的路径积分计算中,重点关注三维时空以简化角动量的处理。
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来源期刊
Journal of High Energy Physics
Journal of High Energy Physics 物理-物理:粒子与场物理
CiteScore
10.30
自引率
46.30%
发文量
2107
审稿时长
1.5 months
期刊介绍: The aim of the Journal of High Energy Physics (JHEP) is to ensure fast and efficient online publication tools to the scientific community, while keeping that community in charge of every aspect of the peer-review and publication process in order to ensure the highest quality standards in the journal. Consequently, the Advisory and Editorial Boards, composed of distinguished, active scientists in the field, jointly establish with the Scientific Director the journal''s scientific policy and ensure the scientific quality of accepted articles. JHEP presently encompasses the following areas of theoretical and experimental physics: Collider Physics Underground and Large Array Physics Quantum Field Theory Gauge Field Theories Symmetries String and Brane Theory General Relativity and Gravitation Supersymmetry Mathematical Methods of Physics Mostly Solvable Models Astroparticles Statistical Field Theories Mostly Weak Interactions Mostly Strong Interactions Quantum Field Theory (phenomenology) Strings and Branes Phenomenological Aspects of Supersymmetry Mostly Strong Interactions (phenomenology).
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