We review results for the phase diagram of QCD, the properties of quarks and gluons and the resulting properties of strongly interacting matter at finite temperature and chemical potential. The interplay of two different but related transitions in QCD, chiral symmetry restoration and deconfinement, leads to a rich phenomenology when external parameters such as quark masses, volume, temperature and chemical potential are varied. We discuss the progress in this field from a theoretical perspective, focusing on non-perturbative QCD as encoded in the functional approach via Dyson-Schwinger and Bethe-Salpeter equations. We aim at a pedagogical overview on the physics associated with the structure of this framework and explain connections to other approaches, in particular with the functional renormalization group and lattice QCD. We discuss various aspects associated with the variation of the quark masses, assess recent results for the QCD phase diagram including the location of a putative critical end-point for $N_f=2+1$ and $N_f=2+1+1$, discuss results for quark spectral functions and summarise aspects of QCD thermodynamics and fluctuations.

中文翻译：

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来自 Dyson-Schwinger 方程的有限温度和化学势下的 QCD

我们回顾了 QCD 相图的结果、夸克和胶子的性质以及在有限温度和化学势下强相互作用物质的所得性质。当夸克质量、体积、温度和化学势等外部参数发生变化时，QCD 中两种不同但相关的跃迁（手性对称恢复和去限制）的相互作用导致了丰富的现象学。我们从理论角度讨论该领域的进展，重点关注通过 Dyson-Schwinger 和 Bethe-Salpeter 方程在函数方法中编码的非微扰 QCD。我们的目标是对该框架结构相关的物理学进行教学概述，并解释与其他方法的联系，特别是与功能重整化组和晶格 QCD 的联系。