Roberge-Weiss phase transitions and extended Z3 symmetry
H. Kouno, Y. Sakai, K. Kashiwa, M. Matsuzaki, M. Yahiro
备注：
3 pages, 1 figure, to be published in the proceedings for the YITP workshop YITP-W-08-09 on "Thermal Quantum Field Theories and Their Applications", Kyoto, September 3-5, 2008
Using the Polyakov extended Nambu-Jona-Lasinio (PNJL) model with imaginary chemical potential, the relation between the Roberge-Weiss (RW) phase transition and the extended Z3 symmetry is studied. At low temperature, there is approximate continuous symmetry under the phase transformation of the Polyakov loop with the shift of the imaginary chemical potential. Due to this continuous symmetry, the Polyakov loop can oscillate smoothly as the imaginary chemical potential increases. At high temperature, this continuous symmetry is broken to an exact discrete symmetry, the extended Z3 symmetry, and the Polyakov loop can not oscillate smoothly. This symmetry breaking of the continuous symmetry causes a discontinuity of the Polyakov loop. That is the RW phase transition.
We study the localization properties of the low-lying Dirac eigenmodes in QCD at imaginary chemical potential $\hatμ_I=π$ at temperatures above the Roberge-Weiss transition temperature $T_{\rm RW}$. We find that modes are localized up to a temperature-dependent "mobility edge" and delocalized above it, and that the mobility edge extrapolates to zero at a temperature compatible with $T_{\rm RW}$. This supports the existence of a strong connection between localization of the low Dirac modes and deconfinement, studied here for the first time in a model with a genuine deconfinement transition in t…
At finite imaginary values of the chemical potential, QCD is free of the sign problem. Moreover, at high temperatures the partition function exhibits a new symmetry (the Roberge-Weiss symmetry) connecting phases with different orientations of the Polyakov loop, and the corresponding phase transitions between these. In this contribution we investigate the perturbative one-loop effective potential for the Polyakov loop in the presence of imaginary isospin as well as baryon chemical potentials. This leads to a novel phase diagram, which reveals an interesting insight about the rich phase structur…
We study the phase diagram of two-flavor massless two-color QCD (QC$_2$D) under the presence of quark chemical potentials and imaginary isospin chemical potentials. At the special point of the imaginary isospin chemical potential, called the isospin Roberge--Weiss (RW) point, two-flavor QC$_2$D enjoys the $\mathbb{Z}_2$ center symmetry that acts on both quark flavors and the Polyakov loop. We find a $\mathbb{Z}_2$ 't Hooft anomaly of this system, which involves the $\mathbb{Z}_2$ center symmetry, the baryon-number symmetry, and the isospin chiral symmetry. Anomaly matching, therefore, constrai…
Ample numerical evidence from lattice calculations shows a strong connection between the confining properties of gauge theories at finite temperature and the localisation properties of the low-lying Dirac eigenmodes. In this contribution we discuss recent progress on this topic, focussing on results for QCD at imaginary chemical potential $μ_I/T = π$ at temperatures above the Roberge-Weiss transition temperature. These confirm the general picture of low modes turning from delocalised to localised at the deconfinement transition, in a previously unexplored setup with a genuine, physical transit…
To obtain deeper understanding of QCD properties at finite temperature, we consider the Fourier decomposition of the grand-canonical partition function based on the canonical ensemble method via the imaginary chemical potential. Expectation values are, then, represented by summation over each canonical sector. We point out that the modified Polyakov-loop can play an important role in the canonical ensemble; for example, the Polyakov-loop paradox which is known in the canonical ensemble method can be evaded by considering the quantity. In addition, based on the periodicity issue of the modified…
We discuss the interplay between chiral and center sector phase transitions that occur in QCD with an imaginary quark chemical potential $μ=i(2n+1) πT/3$. Based on a finite size scaling analysis in (2+1)-flavor QCD using HISQ fermions with a physical strange quark mass and a range of light quark masses, we show that the endpoint of the line of first-order Roberge-Weiss (RW) transitions between center sectors is second order for light quark masses $m_l\ge m_s/320$, and that it belongs to the $3$-d, $Z(2)$ universality class. The operator for the chiral condensate behaves like an energy-like ope…
We study how the Roberge-Weiss (RW) transition depends on the pattern of center symmetry breaking using a $\mathbb{Z}_{3}$-QCD model. We adopt flavor-dependent quark imaginary chemical potentials, namely $(μ_{u},μ_{d},μ_{s})/iT=(θ-2π{C}/3,\,θ,\,θ+2π{C}/3)$ with $C\in[0,1]$. The RW periodicity is guaranteed and the center symmetry of $\mathbb{Z}_{3}$-QCD is explicitly broken when $C\neq{1}$ or/and quark masses are non-degenerate. For $N_{f}=3$ and $C\neq{1}$, the RW transition occurs at $θ=θ_{RW}=(2k+1)π/3\,(k\in\mathbb{Z})$, which becomes stronger with decrease of $C$. When $C={1}$, the $θ_{RW…
Phase structure of magnetized quark matter at imaginary chemical potential
Instituto de Física La Plata, CONICET − - Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La PLata（拉普拉塔物理研究所，阿根廷国家科学研究委员会，拉普拉塔国立大学理学院物理系）；CONICET（阿根廷国家科学研究委员会）；Physics Department, Comisión Nacional de Energía Atómica（阿根廷国家原子能委员会物理系）
We present results from an ongoing study of the phase diagram of (2+1)-flavor QCD using the HISQ action with smaller than physical light quark masses in the Roberge-Weiss (RW) plane on lattices with temporal extent $N_τ=4$. We find that the endpoint of the $1^{st}$ order RW transition line remains $2^{nd}$ order at least down to light quark masses corresponding to Goldstone pion masses of $55$ MeV. Furthermore, we show that the chiral condensate is sensitive to the RW transition and may serve as a energy-like operator characterizing universal behavior close to the RW endpoint.
We study an 't Hooft anomaly of massless QCD at finite temperature. With the imaginary baryon chemical potential at the Roberge-Weiss point, there is a $\mathbb{Z}_2$ symmetry which can be used to define confinement. We show the existence of a mixed anomaly between the $\mathbb{Z}_2$ symmetry and the chiral symmetry, which gives a strong relation between confinement and chiral symmetry breaking. The anomaly is a parity anomaly in the QCD Lagrangian reduced to three dimensions. It is reproduced in the chiral Lagrangian by a topological term related to Skyrmion charge, matching the anomaly befor…
Gauge-invariant screening masses and static quark free energies in $N_f = 2+1$ QCD at non-zero baryon density
我们讨论了夸克-胶子等离子体中规范不变的电磁屏蔽质量在有限重子密度情况下的推广，用Polyakov圈子矩阵定义它们。我们给出了具有物理夸克质量的$N_f=2+1$ QCD的格点结果，用虚化学势方法得到，结果表明屏蔽质量随$μ_B$的增加而增加。一个单独的分析进行了理论上有趣的情况下$μ_B/T=3 i π$，其中电荷共轭没有明确打破和通常的定义的屏蔽质量可以用于温度低于罗伯特-魏斯过渡。最后，我们研究了静态夸克自由能对重子化学势的依赖关系，表明它是$μ_B$的递减函数，并在接近$μ_B=0$的赝临界转变温度时表现出特殊的行为。
We investigate the Fourier coefficients $b_k(T)$ of the net--baryon number density in strongly interacting matter at nonzero temperature and density. The asymptotic behavior of the coefficients at large $k$ is determined by the singularities of the partition function in the complex chemical potential plane. Within a QCD-like effective chiral model, we show that the chiral and deconfinement properties at nonzero baryon chemical potential are reflected in characteristic $k$-- and $T$-- dependences of the Fourier coefficients. We also discuss the influence of the Roberge-Weiss transition on these…
We present here the results from an ongoing determination of the critical quark mass in simulations of (2+1)-flavor QCD with an imaginary chemical potential. Studies with unimproved actions found the existence of a critical quark mass value at which the crossover transition ends on a second order phase transition and becomes first order for smaller values of the quark mass for the case of both vanishing and imaginary chemical potential. We use the Highly Improved Staggered Quark (HISQ) action and perform calculations in the Roberge-Weiss (RW) plane, where the value of the critical mass is expe…
Thermodynamic geometry in hadron resonance gas model at real and imaginary baryon chemical potential and a simple sufficient condition for quark deconfinement
Saga University（佐贺大学）；Khazar University（阿塞拜疆坎扎尔大学）；Fukuoka Institute of Technology（福冈工业大学）
