Spontaneous Parity Breaking Research Articles

On the one-dimensional Coulomb problem

We analyse the one-dimensional Coulomb problem (1DCP) pointing out some mistaken beliefs on it. We show that no eigenstates of even or odd parity can represent states of the system. The 1DCP exhibits a sort of spontaneous breaking of parity. We also show that a superselection rule operates in the system. Such rule explains some of its peculiarities. We build the superpotential associated to the 1DCP.

Spontaneous parity violation in a supersymmetric left–right symmetric model

We propose a novel implementation of spontaneous parity breaking in supersymmetric left–right symmetric model, avoiding some of the problems encountered in previous studies. This implementation includes a bi-triplet and a singlet, in addition to the bi-doublets which extend the Higgs sector of the Minimal Supersymmetric Standard Model (MSSM). The supersymmetric vacua of this theory are shown to lead generically to spontaneous violation of parity, while preserving R-parity. The model is shown to reproduce the see-saw relation for vacuum expectation values, vLvR≈mEW2 relating the new mass scales vL, vR to the electroweak scale mEW, just as in the non-supersymmetric version. The scale vR determines the mass scale of heavy Majorana neutrinos, which gets related to the observed neutrino masses through type II see-saw relation.

Consistency of the Aoki phase

Lattice QCD with two flavors of Wilson fermions can exhibit spontaneous breaking of flavor and parity, with the resulting ``Aoki phase'' characterized by the nonzero expectation value $⟨\overline{\ensuremath{\psi}}{\ensuremath{\gamma}}_{5}{\ensuremath{\tau}}_{3}\ensuremath{\psi}⟩\ensuremath{\ne}0$. This phenomenon can be understood using the chiral effective theory appropriate to the Symanzik effective action. Within this standard analysis, the flavor-singlet pseudoscalar expectation value vanishes: $⟨i\overline{\ensuremath{\psi}}{\ensuremath{\gamma}}_{5}\ensuremath{\psi}⟩=0$. A recent reanalysis has questioned this understanding, arguing that either the Aoki phase is unphysical, or that there are additional phases in which $⟨i\overline{\ensuremath{\psi}}{\ensuremath{\gamma}}_{5}\ensuremath{\psi}⟩\ensuremath{\ne}0$. The reanalysis uses the properties of probability distribution functions for observables built of fermion fields and expansions in terms of the eigenvalues of the Hermitian Wilson-Dirac operator. Here I show that the standard understanding of the Aoki phase can, in fact, be consistent with the approach used in the reanalysis. Furthermore, if one assumes that the standard understanding is correct, one can use the methods of the reanalysis to derive lattice generalizations of the continuum sum rules of Leutwyler and Smilga.

An upper limit to the electric dipole moment of the neutron from lattice QCD

A linear increase with the volume of the topological susceptibility can signal spontaneous breaking of parity P and time inversion T , due to a nonzero vacuum expectation value of the topological charge Q . Such a breaking would produce a nonzero electric dipole moment of the neutron, d n . An upper limit to d n is derived from numerical simulations at increasing volumes.

Spontaneous parity violation and minimal Higgs models

In this paper we present a model for the spontaneous breaking of parity with two Higgs doublets and two neutral Higgs singlets which are even and odd under D-parity. The condition $ v_R >>v_L $ can be satisfied without introducing bidoublets and it is induced by the breaking of D-parity through the vacuum expectation value of the odd Higgs singlet. Examples of left-right symmetric and mirror fermions models in grand unified theories are presented.

Analyticity inθon the lattice and the large volume limit of the topological susceptibility

Nonanalyticity of QCD with a $\ensuremath{\theta}$ term at $\ensuremath{\theta}=0$ may signal a spontaneous breaking of both parity and time reversal invariance. We address this issue by investigating the large volume limit of the topological susceptibility $\ensuremath{\chi}$ in pure SU(3) gauge theory. We obtain an upper bound for the symmetry breaking order parameter $⟨Q⟩$ and, as a by-product, the value $\ensuremath{\chi}=[173.4(\ifmmode\pm\else\textpm\fi{}0.5)(\ifmmode\pm\else\textpm\fi{}1.2){(}_{\ensuremath{-}0.2}^{+1.1})\text{ }\mathrm{M}\mathrm{e}\mathrm{V}{]}^{4}$ at $\ensuremath{\beta}=6$ ($a\ensuremath{\approx}0.1$ Fermi). The errors are the statistical error from our data, the one derived from the value used for ${\ensuremath{\Lambda}}_{L}$ and an estimate of the systematic error, respectively.

Vafa-Witten theorem on spontaneous breaking of parity

We reexamine the proof provided by Vafa and Witten that there is no spontaneous parity breaking in theories with vectorlike fermions. We argue that the various criticisms that have been leveled at the original proof do not invalidate it.

On absence of spontaneous parity breaking in QCD

We argue that the Vafa–Witten proof on absence of spontaneous parity breaking in QCD has the following two loopholes: first, when perturbed by an external field coupled to a parity-odd quark operator, the QCD vacuum energy could be a decreasing function of the field, contrary to the observation used in the proof. The difference comes from that the effective gluonic operator has in general a parity-even part which does not contribute to the path integral as a pure phase. Second, when perturbed by an external field coupled to a parity-odd gluonic operator, the vacuum energy is always a rising function of the field, independent of the existence of spontaneous parity breaking. This is because the parity-odd gluonic perturbations contribute to the path integral as a pure phase, and could not serve to select a physical vacuum should parity be spontaneously broken.

The ν=5/2 quantum Hall state revisited: spontaneous breaking of the chiral fermion parity and phase transition between Abelian and non-Abelian statistics

We review a recent development in the theoretical understanding of the ν=5/2 quantum Hall plateau and propose a new conformal field theory, slightly different from the Moore–Read one, to describe another universality class relevant for this plateau. The ground state is still given by the Pfaffian and is completely polarized, however, the elementary quasiholes are charge 1/2 anyons with Abelian statistics θ= π/2, which obey complete spin–charge separation. The physical hole is represented by two such quasiholes plus a free neutral Majorana fermion. We also compute the periods and amplitudes of the chiral persistent currents in both states and show that they have different temperature dependence. Finally, we find indications of a classical two-step phase transition between the new and the Moore–Read states, through a compressible state, which is characterized by the spontaneous breaking of a hidden Z 2 symmetry corresponding to the conservation of the chiral fermion parity. We believe that this transition could explain the “kink” observed in the activation experiment for ν=5/2.

Chiral order of spin-1/2 frustrated quantum spin chains

The ordering of the frustrated S = 1/2 XY spin chain with the competing nearest- and next-nearest-neighbor anti-ferromagnetic couplings, J1 and J2, is studied by using the density-matrix renormalization-group method. It is found that besides the well-known spin-fluid and dimer phases the chain exhibits a gapless "chiral" phase characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, κl =SxlSyl+1 – Syl Sxl+1, whereas the spin correlation decays algebraically. The dimer phase is realized for 0.33 [Formula: see text] j = J2/J1 [Formula: see text] 1.26 while the chiral phase is realized for j [Formula: see text] 1.26. PACS No.: 75.25

Dynamical Symmetry Breaking in QED3 from the Wilson RG Point of View

Dynamical symmetry breaking in three dimensional QED with $N$ flavors, which has been mostly analyzed by solving the Schwinger-Dyson equations, is investigated by means of the approximated Wilson, or non-perturbative, renormalization group (RG). We study the RG flows of the gauge coupling and the general four-fermi couplings allowed by the symmetry with concentrating our interest on study of the phase structure. The RG equations have no gauge parameter dependence in our approximation scheme. It is found that there exist chirally broken and unbroken phases for $N > N_{\rm cr}$ ($3 < N_{\rm cr} < 4$) and that the unbroken phase disappears for $N < N_{\rm cr}$. We also discuss the spontaneous parity breaking in three dimensional QED with the four-fermi interactions.

Fermion masses in a model for spontaneous parity breaking

In this paper we discuss a left-right symmetric model for elementary particles and their connection with the mass spectrum of elementary fermions. The model is based on the group $SU(2)_L\otimes SU(2)_R\otimes U(1)$. New mirror fermions and a minimal set of Higgs particles that breaks the symmetry down to $U(1)_{em}$ are proposed. The model can accommodate a consistent pattern for charged and neutral fermion masses as well as neutrino oscillations. An important consequence of the model is that the connection between the left and right sectors can be done by the neutral vector gauge bosons Z and a new heavy Z'.

Chiral order of spin-1/2 frustrated quantum spin chains

The ordering of the frustrated S=1/2 XY spin chain with the competing nearest- and next-nearest-neighbor antiferromagnetic couplings, J_1 and J_2, is studied by using the density-matrix renormalization-group method. It is found that besides the well-known spin-fluid and dimer phases the chain exhibits gapless `chiral' phase characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, \kappa _l=S_l^xS_{l+1}^y-S_l^yS_{l+1}^x, whereas the spin correlation decays algebraically. The dimer phase is realized for 0.33 \lsim j = J_2/J_1 \lsim 1.26 while the chiral phase is realized for j \gsim 1.26.

No-go theorem on spontaneous parity breaking revisited

An essential assumption in the Vafa and Witten's theorem on P and CT realization in vector-like theories concerns the existence of a free energy density in Euclidean space in the presence of any external hermitian symmetry breaking source. We show how this requires the previous assumption that the symmetry is realized in the vacuum. Even if Vafa and Witten's conjecture is plausible, actually a theorem is still lacking.

No-go theorem on spontaneous parity breaking revisited

No-go theorem on spontaneous parity breaking revisited

Orthogonal ensemble of random matrices and QCD in three dimensions

We consider the parity-invariant Dirac operator with a mass term in three-dimensional QCD for $N_c=2$ and quarks in the fundamental representation. We show that there exists a basis in which the matrix elements of the Euclidean Dirac operator are real. Assuming there is spontaneous breaking of flavor and/or parity, we read off from the fermionic action the flavor symmetry-breaking pattern $Sp(4N_f) \to Sp(2N_f) \times Sp(2N_f)$ that might occur in such a theory. We then construct a random matrix theory with the same global symmetries as two-color QCD$_3$ with fundamental fermions and derive from here the finite-volume partition function for the latter in the static limit. The expected symmetry breaking pattern is confirmed by the explicit calculation in random matrix theory. We also derive the first Leutwyler-Smilga-like sum rule for the eigenvalues of the Dirac operator.

Ground State Phase Diagram of Frustrated S = 1 XXZ chains: Chiral Ordered Phases

The ground-state phase diagram of frustrated S=1 XXZ spin chains with the competing nearest- and next-nearest-neighbor antiferromagnetic couplings is studied using the infinite-system density-matrix renormalization-group method. We find six different phases, namely, the Haldane, gapped chiral, gapless chiral, double Haldane, N\'{e}el, and double N\'{e}el (uudd) phases. The gapped and gapless chiral phases are characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, \kappa_l = S_l^xS_{l+1}^y-S_l^yS_{l+1}^x, whereas the spin correlation decays either exponentially or algebraically. These chiral ordered phases appear in a broad region in the phase diagram for \Delta < 0.95, where \Delta is an exchange-anisotropy parameter. The critical properties of phase transitions are also studied.

Spin and Chiral Orderings of Frustrated Quantum Spin Chains

Ordering of frustrated S=1/2 and 1 XY and Heisenberg spin chains with the competing nearest- and next-nearest-neighbor antiferromagnetic couplings is studied by exact diagonalization and density-matrix renormalization-group methods. It is found that the S=1 XY chain exhibits both gapless and gapped `chiral' phases characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, $\kappa_i = S_i^xS_{i+1}^y-S_i^yS_{i+1}^x$, whereas the spin correlation decays either algebraically or exponentially. Such chiral phases are not realized in the S=1/2 XY chain nor in the Heisenberg chains.

Spontaneous time reversal and parity breaking in a d x2– y2-WAVE superconductor with magnetic impurities

It is argued that the d x 2– y 2 superconductor exhibits a transition into the d x 2– y 2 +id xy state in the presence of magnetic impurities in certain conditions. Linear coupling between impurity magnetization and the d xy component drives this transition. Violation of time-reversal symmetry and parity occurs spontaneously via the second order transition. In the ordered phase both impurity magnetization and d xy component of the order parameter develop and are proportional to each other.

Spontaneous flavor and parity breaking with Wilson fermions

We discuss the phase diagram of Wilson fermions in the ${m}_{0}\ensuremath{-}{g}^{2}$ plane for two-flavor QCD. We argue that, as originally suggested by Aoki, there is a phase in which flavor and parity are spontaneously broken. Recent numerical results on the spectrum of the overlap Hamiltonian have been interpreted as evidence against Aoki's conjecture. We show that they are in fact consistent with the presence of a flavor-parity broken ``Aoki phase.'' We also show how, as the continuum limit is approached, one can study the lattice theory using the continuum chiral Lagrangian supplemented by additional terms proportional to powers of the lattice spacing. We find that there are two possible phase structures at non-zero lattice spacing: (1) there is an Aoki phase of width $\ensuremath{\Delta}{m}_{0}\ensuremath{\sim}{a}^{3}$ with two massless Goldstone pions; (2) there is no symmetry breaking, and all three pions have an equal non-vanishing mass of order $a.$ Present numerical evidence suggests that the former option is realized for Wilson fermions. Our analysis then predicts the form of the pion masses and the flavor-parity breaking condensate within the Aoki phase. Our analysis also applies for non-perturbatively improved Wilson fermions.