Chiral Symmetry Breaking Phase Research Articles

Two-dimensional model with chiral condensates and Cooper pairs having a QCD-like phase structure

We generalize our previous model to an O(N) symmetric two-dimensional model which possesses chiral symmetry breaking and superconducting (Cooper pair condensates) phases at large-N. At zero temperature and density, the model can be solved analytically in the large-N limit. We perform the renormalization explicitly and obtain a closed form expression of the effective potential. There exists a renormalization group invariant parameter $\delta$ that determines which of the condensates exist in the vacuum. At finite temperatures and densities, we map out the phase structure of the model by a detailed numerical analysis of the renormalized effective potential. For $\delta$ positive and sufficiently large, the phase diagram in the $\mu$-$T$ (chemical potential-temperature) plane exactly mimics the features expected for QCD with two light flavors of quarks. At low temperatures there exists low-$\mu$ chiral symmetry breaking and high-$\mu$ Cooper pair condensate regions which are separated by a first-order phase transition. At high $\mu$, when the temperature is raised, the system undergoes a second-order phase transition from the superconducting phase to an unbroken phase in which both condensates vanish. For a range of values of $\delta$ the theory possesses a tricritical point ($\mu_{tc}$ and $T_{tc}$); for $\mu > \mu_{tc}$ ($\mu < \mu_{tc}$) the phase transition from the low temperature chiral symmetry breaking phase to unbroken phase is first-order (second-order). For the range of $\delta$ in which the system mimics QCD, we expect the model to be useful for the investigation of dynamical aspects of nonequilibrium phase transitions, and to provide information relevant to the study of relativistic heavy ion collisions and the dense interiors of neutron stars.

Quark confinement and deconfinement in QCD from the viewpoint of Abelian-projected effective gauge theory

We give another derivation of quark confinement in QCD from the viewpoint of the low-energy effective Abelian gauge theory of QCD obtained via Abelian projection. It is based on the recently discovered Berezinskii-Kosterlitz-Thouless phase transition in the four-dimensional Abelian gauge theory. Moreover, we show that there exists a critical gauge coupling constant in QCD, above which confinement set in and below which there is no confinement. In a SU( N) gauge theory with N f flavored fermions, we argue that this leads to a critical value of fermion flavors N f c for the confinement as well as the chiral symmetry breaking, which separates the deconfining and chiral symmetric phase from the confining and chiral symmetry breaking phase. A finite-temperature deconfinement transition is also discussed briefly.

Anomalous global strings and primordial magnetic fields

We propose a new mechanism for the generation of primordial magnetic fields, making use of the magnetic fields which are induced by anomalous global strings which couple to electromagnetism via Wess-Zumino type interactions. This mechanism can be realized in QCD by utilizing pion strings, global vortices which appear in the linear sigma model which describes physics below the QCD confinement scale. During the chiral symmetry breaking phase transition, pion strings can be produced, thus leading to primordial magnetic fields. We calculate the magnitude and coherence length of these fields. They are seen to depend on the string dynamics. With optimistic assumptions, both the magnitude and coherence scale of the induced magnetic fields can be large enough to explain the seed magnetic fields of greater than $10^{-23}$ Gauss necessary to produce the observed galactic magnetic fields via the galactic dynamo mechanism.

ε-EXPANSION IN QUANTUM FIELD THEORY IN CURVED SPACE–TIME

We discuss ε-expansion in curved space–time for asymptotically free and asymptotically nonfree theories. The existence of stable and unstable fixed points is investigated for fϕ4 theory and SU(2) gauge theory. It is shown that ε-expansion maybe compatible with aysmptotic freedom on special solutions of the RG equations in a special ase (supersymmetric theory). Using ε-expansion RG technique, the effective Lagrangian for covariantly constant gauge SU(2) field and effective potential for gauged NJL model are found in (4-ε)-dimensional curved space (in linear curvature approximation). The curvature-induced phase transitions from symmetric phase to asymmetric phase (chromomagnetic vacuum and chiral symmetry broken phase, respectively) are discussed for the above two models.

Quantum critical phenomena: The relationship between spin systems and strongly coupled gauge theories

Abstract In this set of lectures, I shall review some recent work on quantum critical phenomena which involve the changes in phase of the ground state of a quantum antiferromagnetic system when external parameters are varied through some critical values. I will also draw analogies between antiferromagnetic phase transitions and chiral phase transitions in lower (particularly 2 + l)-dimensional gauge theories and also some 2+1-dimensional four-fermi theories where chiral symmetry breaking patterns depend on the coupling constants and also the matter and gauge field content of the theory. I will begin by reviewing some arguments that, in the infrared limit, the dynamics of Goldstone bosons in the confining and chiral symmetry breaking phase of 2 + 1 dimensional QCD is identical to the effective spin wave dynamics in 2 dimensional generalized quantum antiferromagnets. I also discuss the possibility that certain quantum critical behaviors in generalized antiferromagnets can be analyzed using the principle of ...

Chiral transition in a strongly coupled fermion-gauge-scalar model

We report the recent results from the computer simulations of a fermion-gauge-scalar model with dynamical chiral-symmetry breaking and chiral transition induced by the scalar field. This model might be considered to be a possible alternative to the Higgs mechanism of mass generation. A new scheme is developed for detecting the chiral transition. Our results show with higher precision than the earlier works that the chiral transition line joins the Higgs phase transition line, separating the Higgs and Nambu (chiral-symmetry breaking) phases. The end point of the Higgs transition with divergent correlation lengths is therefore suitable for an investigation of the continuum limit.

GAUGE INDEPENDENT PHASE STRUCTURE OF GAUGED NAMBU-JONA-LASINIO AND YUKAWA MODELS

We investigate the critical behavior of the gauged NJL model (QED plus four-fermion interaction) and the gauged Yukawa model by the use of the inversion method. By calculating the gauge-invariant chiral condensate in the inversion method to the lowest order, we derive the critical line which separates the spontaneous chiral-symmetry breaking phase from the chiral symmetric one. The critical exponent for the chiral order parameter associated with the second order chiral phase transition is shown to take the mean field value together with possible logarithmic correction to the mean-field prediction. All the above results are gauge-parameter independent and are compared with the previous results obtained from the Schwinger-Dyson equation for the fermion propagator.

Staggered fermions and chiral-symmetry breaking in transverse lattice regulated QED.

Staggered fermions are constructed for the transverse lattice regularization scheme. The weak perturbation theory of transverse lattice non-compact QED is developed in light-cone gauge, and we argue that for fixed lattice spacing this theory is ultraviolet finite, order by order in perturbation theory. However, by calculating the anomalous scaling dimension of the link fields, we find that the interaction Hamiltonian becomes non-renormalizable for $g^2(a) > 4\pi$, where $g(a)$ is the bare (lattice) QED coupling constant. We conjecture that this is the critical point of the chiral symmetry breaking phase transition in QED. Non-perturbative chiral symmetry breaking is then studied in the strong coupling limit. The discrete remnant of chiral symmetry that remains on the lattice is spontaneously broken, and the ground state to lowest order in the strong coupling expansion corresponds to the classical ground state of the two-dimensional spin one-half Heisenberg antiferromagnet.

STRONG COUPLING QED BREAKS CHIRAL SYMMETRY

We show that the strong coupling limit of d-dimensional quantum electrodynamics with 2d/2[d/2] flavors of fermions can be mapped onto the s=1/2 quantum Heisenberg antiferromagnet in d–1 space dimensions. We use this mapping to prove that the strong coupling limit of QED breaks chiral symmetry. The staggered Néel order parameter of the antiferromagnet is the expectation value of a mass operator in QED and the spin-waves are pions. We speculate that the chiral symmetry breaking phase transition corresponds to a transition between the flux phase and the conventional Néel ordered phase of an antiferromagnetic t-J model.

Topological fluctuations in SU(2) gauge theory with staggered fermions: An explotary study

We investigate some basic aspects of topological fluctuations in lattice QCD, in the version with two colours and four light flavours; and we do so in both the confining, chiral symmetry broken phase and in the non-confining, chirally symmetric phase. This latter phase is found to ccut not only high temperatures, just as in the pure gauge system, but also in small spatial volumes, which is unlike the pure gauge case. We derive the way the topological susceptibility should vary with quark mass at small quark masses. We find that the calculated topological susceptibility decerases to zero with the quark mass, with the theretically expected powers except — in the symmetric phase — at the very smallest values of the quark mass. We demonstrate that this anomalous behaviour can be understood as arising from the fact that the lattice topological “zero modes” are in fact sufficiently far from being zero. We also show, in the chirally symmetric phase, that, just as expected, the average distance between instantons and anti-instantons decreases with decreasing quark mass. We finish with a new and more precise estimate of the location of the finite-temperature transition in SU(2) with four light flavours.

Aspects of dynamical electroweak symmetry breaking

In technicolor models it has recently been suggested that dynamics at scales much higher than the electroweak scale can play a significant role in electroweak symmetry breaking, and that these effects can lead to a heavy top quark while alleviating the flavor changing neutral current problems endemic to extended technicolor theories. In this paper we formulate the conditions necessary for this hierarchy to occur. We show that, if extended technicolor interactions are to play a role in electroweak symmetry breaking and in particular if they are to enhance fermion masses above their values in the usual weak extended technicolor scenario, then the chiral symmetry breaking phase transition must be second order. We also show that the effective low-energy theory below the ETC scale must include both technicolor and a light composite scalar with large couplings to ordinary fermions and technifermions.

Chiral colour dielectric model of the nucleon

Abstract We apply the colour dielectric model to the nucleon including the chiral symmetry by the linear sigma model. The results of numerical calculations show that as the quark-meson coupling becomes stronger, the chiral symmetry breaking phase inside the bag changes to the restoring phase. The hedgehog solution is projected onto the spin-isospin eigenstate by means of the collective coordinate method, and we study some static properties of the nucleon. Except for the proton magnetic moment, the observed static properties favour strong quark-meson coupling and light glueball mass (∼1 GeV) giving a “chiral bag” like solution. The calculated values of the observables are similar to those of the chiral soliton bag model with the topological number: Z = 1.

The chiral transition in an SU(2) gauge-Higgs-fermion theory with Yukawa couplings

We study the (zero-temperature) chiral transition in an SU(2) lattice gauge theory with I = 1 2 Higgs fields, and fermion fields with I = 1 2 and I = 0 , including Yukawa couplings. Using analytic methods in the strong gauge coupling limit, we demonstrate that (i) if at least one of the Yukawa couplings is sufficiently weak, this theory undergoes a spontaneous chiral symmetry breaking phase transition; (ii) this transition is removed when the Yukawa couplings are sufficiently strong. The transition is determined to be of second order, and approximate critical point calculations are given. Some implications for the continuum limit of the SU(2) model, and for electroweak interactions, are discussed.

On anomalous U(1) gauge theory in four dimensions

We discuss the consistency, unitarity and Lorentz invariance of an anomalous U(1) gauge theory in four dimensions. Our analysis is based on an effective low-energy action valid in the chiral symmetry broken phase. The allegedly bad properties of anomalous theories (except non-renormalizability) are examined. It is shown that, in the low-energy context, the theory can be consistently and unitarily quantised, and is formally Lorentz covariant.

Strong interactions at all densities in a chiral soliton model coupled to quarks

In the context of a linear chiral σ-model coupled to quarks we argue that the single baryon and high density ground state occurs in a topological chiral symmetry (TCB) broken phase and not the usual space uniform (UCB) chiral symmetry broken phase. We expect this to transit directly to a QCD chirally restored phase at higher density. New, but plausible features of dense matter in this phase are highlighted and it is shown that known features of nuclear matter can be recovered.

Phase transition in the lattice gross-neveu model

We show that for N=∞, the N-component lattice Gross-Neveu model is equivalent to an Ising model, and thus has a (chiral symmetry breaking) phase transition.