Dimensional reduction in finite-temperature quantum chromodynamics. II

1988 ◽  
Vol 38 (10) ◽  
pp. 3287-3294 ◽  
Author(s):  
Sudhir Nadkarni
Keyword(s):  
Quantum Chromodynamics ◽  
Dimensional Reduction ◽  
Finite Temperature

scholarly journals Effective String Description of the Confining Flux Tube at Finite Temperature

Universe ◽  
2021 ◽  
Vol 7 (6) ◽  
pp. 170
Author(s):  
Michele Caselle
Keyword(s):  
Flux Tube ◽  
Dimensional Reduction ◽  
Conformal Invariance ◽  
Finite Temperature ◽  
Gauge Theories ◽  
Linear Increase ◽  
General Introduction ◽  
Interquark Potential ◽  
Effective String Theory ◽  
Good Agreement

In this review, after a general introduction to the effective string theory (EST) description of confinement in pure gauge theories, we discuss the behaviour of EST as the temperature is increased. We show that, as the deconfinement point is approached from below, several universal features of confining gauge theories, like the ratio Tc/σ0, the linear increase of the squared width of the flux tube with the interquark distance, or the temperature dependence of the interquark potential, can be accurately predicted by the effective string. Moreover, in the vicinity of the deconfinement point the EST behaviour turns out to be in good agreement with what was predicted by conformal invariance or by dimensional reduction, thus further supporting the validity of an EST approach to confinement.

Quantum field theory (QFT) at finite temperature: Equilibrium properties

2021 ◽  
pp. 786-830
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Transitions ◽  
High Temperature ◽  
Dimensional Reduction ◽  
Finite Temperature ◽  
Finite Size ◽  
Quantum Field ◽  
Statistical Field ◽  
Statistical Field Theory

Some equilibrium properties in statistical quantum field theory (QFT), that is, relativistic QFT at finite temperature are reviewed. Study of QFT at finite temperature is motivated by cosmological problems, high energy heavy ion collisions, and speculations about possible phase transitions, also searched for in numerical simulations. In particular, the situation of finite temperature phase transitions, or the limit of high temperature (an ultra-relativistic limit where the temperature is much larger than the physical masses of particles) are discussed. The concept of dimensional reduction emerges, in many cases, statistical properties of finite-temperature QFT in (1, d − 1) dimensions can be described by an effective classical statistical field theory in (d − 1) dimensions. Dimensional reduction generalizes a property already observed in the non-relativistic example of the Bose gas, and indicates that quantum effects are less important at high temperature. The corresponding technical tools are a mode-expansion of fields in the Euclidean time variable, singling out the zero modes of boson fields, followed by a local expansion of the resulting (d − 1)-dimensional effective field theory (EFT). Additional physical intuition about QFT at finite temperature in (1, d−1) dimensions can be gained by considering it as a classical statistical field theory in d dimensions, with finite size in one dimension. This identification makes an analysis of finite temperature QFT in terms of the renormalization group (RG), and the theory of finite-size effects of the classical theory, possible. These ideas are illustrated with several simple examples, the φ4 field theory, the non-linear σ-model, the Gross–Neveu model and some gauge theories.

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