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Register a new userPhase Structure of QED3 at Finite Temperature
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Dynamical symmetry breaking in three-dimensional QED with N fermion flavours is considered at finite temperature, in the large $N$ approximation. Using an approximate treatment of the Schwinger-Dyson equation for the fermion self-energy, we find that chiral symmetry is restored above a certain critical temperature which depends itself on $N$. We find that the ratio of the zero-momentum zero-temperature fermion mass to the critical temperature has a large value compared with four-fermion theories, as had been suggested in a previous work with a momentum-independent self-energy. Evidence of a temperature- dependent critical $N$ is shown to appear in this approximation. The phase diagram for spontaneous mass generation in the theory is presented in $T-N$ space.
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A recent study of dynamical chiral symmetry breaking in N-flavour QED$_3$ at finite temperature is extended to include the effect of fermion wavefunction renormalisation in the Schwinger-Dyson equations. The simple ``zero-frequency truncation previously used is found to lead to unphysical results, especially as $T to 0$. A modified set of equations is proposed, whose solutions behave in a way which is qualitatively similar to the $T=0$ solutions of Pennington et al. [5-8] who have made extensive studies of the effect of wavefunction renormalisation in this context, and who concluded that there was no critical $N_c$ (at T=0) above which chiral symmetry was restored. In contrast, we find that our modified equations predict a critical $N_c$ at $T ot= 0$, and an $N-T$ phase diagram very similar to the earlier study neglecting wavefunction renormalisation. The reason for the difference is traced to the different infrared behaviour of the vacuum polarisation at $T=0$ and at $T ot= 0$.
We discuss the phase structure of QCD for $N_f=2$ and $N_f=2+1$ dynamical quark flavours at finite temperature and baryon chemical potential. It emerges dynamically from the underlying fundamental interactions between quarks and gluons in our work. To this end, starting from the perturbative high-energy regime, we systematically integrate-out quantum fluctuations towards low energies by using the functional renormalisation group. By dynamically hadronising the dominant interaction channels responsible for the formation of light mesons and quark condensates, we are able to extract the phase diagram for $mu_B/T lesssim 6$. We find a critical endpoint at $(T_text{CEP},{mu_B}_{text{CEP}})=(107, 635),text{MeV}$. The curvature of the phase boundary at small chemical potential is $kappa=0.0142(2)$, computed from the renormalised light chiral condensate $Delta_{l,R}$. Furthermore, we find indications for an inhomogeneous regime in the vicinity and above the chiral transition for $mu_Bgtrsim 417$ MeV. Where applicable, our results are in very good agreement with the most recent lattice results. We also compare to results from other functional methods and phenomenological freeze-out data. This indicates that a consistent picture of the phase structure at finite baryon chemical potential is beginning to emerge. The systematic uncertainty of our results grows large in the density regime around the critical endpoint and we discuss necessary improvements of our current approximation towards a quantitatively precise determination of QCD phase diagram.
We demonstrate the applicability of integration-by-parts (IBP) identities in finite-temperature field theory. As a concrete example, we perform 3-loop computations for the thermodynamic pressure of QCD in general covariant gauges, and confirm earlier Feynman-gauge results.
We analyze the electroweak phase transition at finite temperature in a model of gauge-Higgs unification where the fermion mass hierarchy including top quark mass, a viable electroweak symmetry breaking and an observed Higgs mass are successfully reproduced. To study the phase transition, we derive the general formula of the 1-loop effective potential at finite temperature by using the $zeta$ function regularization method. It is remarkable that the functions determining the Kaluza-Klein mass spectrum have only to be necessary in calculations. This potential can be applicable to any higher dimensional theory in flat space where one extra spatial dimension is compactified. Applying to our model of gauge-Higgs unification, the strong first phase transition compatible with 125 GeV Higgs mass is found to happen.
I review recent developments in the studies of the phase structure and equation of state in finite temperature QCD on the lattice.
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