Modeling finite-volume effects and chiral symmetry breaking in two-flavor QCD thermodynamics

Abstract

Finite-volume effects in Quantum Chromodynamics (QCD) have been a subject of much theoretical interest for more than two decades. They are in particular important for the analysis and interpretation of QCD simulations on a finite, discrete space-time lattice. Most of these effects are closely related to the phenomenon of spontaneous breaking of the chiral flavor symmetry and the emergence of pions as light Goldstone bosons. These long-range fluctuations are strongly affected by putting the system into a finite box, and an analysis with different methods can be organized according to the interplay between pion mass and box size. The finite volume also affects critical behavior at the chiral phase transition in QCD. In the present review, I will be mainly concerned with modeling such finite volume effects as they affect the thermodynamics of the chiral phase transition for two quark flavors.I review recent work on the analysis of finite-volume effects which makes use of the quark-meson model for dynamical chiral symmetry breaking. To account for the effects of critical long-range fluctuations close to the phase transition, most of the calculations have been performed using non-perturbative Renormalization Group (RG) methods. I give an overview over the application of these methods to a finite volume. The method, the model and the results are put into the context of related work in random matrix theory for very small volumes, chiral perturbation theory for larger volumes, and related methods and approaches. They are applied towards the analysis of finite-volume effects in lattice QCD simulations and their interpretation, mainly in the context of the chiral phase transition for two quark flavors.

Chiral transition and the chiral charge density of the hot and dense QCD matter.

“…In this case, the quark and gluon fields take the same boundary condition in their spatial and temporal directions. As pointed out by authors in [66], such choice allows a permutation symmetry of the spatial and temporal directions in the effective Lagrangian, rendering temperature-and volume-independent coupling constants. One can then directly employ models that were determined at zero temperature and volume.…”

Chiral susceptibility in ( 2+1 )-flavor QCD

“…For instance, low-energy effective theory computations indicate that the chiral phase transition temperature in the limit of massless up and down quarks is a possible upper bound for the transition temperature at the critical endpoint; see Refs. [18][19][20][21] for recent works and reviews. Accordingly, the nature of the chiral transition in QCD with three quark flavors is very actively researched.…”

Quantized first-order phase transition and two sets of critical end point in droplet quark matter

“…Applying the anti-periodic and periodic spatial boundary conditions to quarks induces opposite results on vacuum properties: the anti-periodic spatial boundary condition for quarks induces that the chiral symmetry restores in the small system, while the periodic spatial boundary condition induces the enhancement or catalysis of the chiral symmetry breaking in the vacuum. In most cases, the anti-periodic spatial boundary condition has been applied for quarks to keep the permutation symmetry between the time and space directions [29,33]. Another reason of applying the anti-periodic boundary condition to quarks is to get consistent results of volume dependent pion mass from chiral perturbation theory (ChPT) [34], where the pion mass increases with the decrease of the system size.…”