Gliding Down the QCD Transition Line, from Nf = 2 till the Onset of Conformality

Andrey Yu Kotov,Maria Paola Lombardo,Anton Trunin

doi:10.3390/sym13101833

Andrey Yu Kotov, Maria Paola Lombardo + Show 1 more

Open Access

https://doi.org/10.3390/sym13101833

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Abstract

We review the hot QCD transition with varying number of flavours, from two till the onset of the conformal window. We discuss the universality class for Nf=2, along the critical line for two massless light flavours, and a third flavour whose mass serves as an interpolator between Nf=2 and Nf=3. We identify a possible scaling window for the 3D O(4) universality class transition, and its crossover to a mean field behaviour. We follow the transition from Nf=3 to larger Nf, when it remains of first order, with an increasing coupling strength; we summarise its known properties, including possible cosmological applications as a model for a strong electroweak transition. The first order transition, and its accompanying second order endpoint, finally morphs into the essential singularity at the onset of the conformal window, following the singular behaviour predicted by the functional renormalisation group.

Highlights

We review the hot QCD transition with varying number of flavours, from two till the onset of the conformal window
The hot symmetric phase is known as quark gluon plasma; in the chiral limit the phase transitions may be of a second order for N f = 2, probably in the universality class of the three dimensional O(4) ferromagnet
The remaining of this report is organised as follows: we review the theoretical knowledge about the critical line

Summary

Phases of QCD and Critical Behaviour

Strong interactions have different phases in the space of the number of flavours N f , quark mass, temperature [1,2]. At zero temperature the symmetric phase is conformal: it is separated from the broken phase by a conformal phase transition [2,8]—similar to a Berezinskii–Kosterlitz–Thouless (BKT) transition: the scaling of the order parameter reveals an essential singularity. It is not clear—to our knowledge—how the line of first order phase transitions expected at large N f would turn into a conformal transition, and other scenarios are possible, including a power-law scaling [9] and even a first order transition [10,11].

Universal Approach to Phase Transitions

Large N f

Summary