Pattern Of Chiral Symmetry Breaking Research Articles

Patterns of chiral symmetry breaking and a candidate for aCtheorem in four dimensions

We test a candidate for a four-dimensional C function. This is done by considering all asymptotically free, vectorlike gauge theories with ${N}_{f}$ flavors and fermions in arbitrary representations of any simple Lie group. Assuming spontaneous breaking of chiral symmetry in the infrared limit and that the value of the C function in this limit is determined by the number of Goldstone bosons, we find that only in the case of a theory with two colors and fermions in one single pseudoreal representation of SU(2) does the C theorem seem to be violated. Conversely, this might also be a sign of new constraints, restricting the number of flavors consistent with spontaneous chiral symmetry breaking. For all other groups and representations we find that this candidate C function decreases along the renormalization-group flow.

On SUSY breaking and χSB from string duals

We find regular string duals of three-dimensional N=1 SYM with a Chern–Simons interaction at level k for SO and Sp gauge groups. Using the string dual we exactly reproduce the conjectured pattern of supersymmetry breaking proposed by Witten by showing that there is dynamical supersymmetry breaking for k< h/2 while supersymmetry remains unbroken for k⩾ h/2, where h is the dual Coxeter number of the gauge group. We also find regular string duals of four-dimensional N=1 SYM for SO and Sp gauge groups and exactly reproduce the expected pattern of chiral symmetry breaking Z 2 h → Z 2 by analyzing the symmetries of the string solution.

η′Mass and Chiral Symmetry Breaking at LargeNcandNf

We propose a method for implementing the large- N(c), large-N(f) limit of QCD at the effective Lagrangian level. Depending on the value of the ratio N(f)/N(c), different patterns of chiral symmetry breaking can arise, leading in particular to different behaviors of the eta(') mass in the combined large-N limit.

Chiral Lagrangians from lattice gauge theories in the strong coupling limit

We derive nonlinear $\ensuremath{\sigma}$ models (chiral Lagrangians) over symmetric spaces $\mathrm{U}(n),$ $\mathrm{U}(2n)/\mathrm{Sp}(2n),$ and $\mathrm{U}(2n)/\mathrm{O}(2n)$ from $\mathrm{U}(N),$ $\mathrm{O}(N),$ and $\mathrm{Sp}(2N)$ lattice gauge theories coupled to n flavors of staggered fermions, in the large-$N$ and ${g}^{2}N$ limit. To this end, we employ Zirnbauer's color-flavor transformation. We prove the spatial homogeneity of the vacuum configurations of mesons by explicitly solving the large-$N$ saddle point equations, and thus establish these patterns of spontaneous chiral symmetry breaking in the above limit.

Spectra of massive QCD Dirac operators from random matrix theory: all three chiral symmetry breaking patterns

The microscopic spectral eigenvalue correlations of QCD Dirac operators in the presence of dynamical fermions are calculated within the framework of Random Matrix Theory (RMT). Our approach treats the low-energy correlation functions of all three chiral symmetry breaking patterns (labeled by the Dyson index β = 1, 2 and 4) on the same footing, offering a unifying description of massive QCD Dirac spectra. RMT universality is explicitly proven for all three symmetry classes and the results are compared to the available lattice data for β = 4.

One-loop fermion determinant with explicit chiral symmetry breaking

We use a proper-time regularization to define the real part of the one-loop fermion determinant for the case in which explicit chiral symmetry breaking takes place. We demonstrate that beyond the chiral limit the standard definition of Re[lndet D] by ln|det D| deforms the symmetry breaking pattern of the basic fermionic Lagrangian. We show how to obtain the correcting functional in order to arrive at the fermion determinant whose transformation properties are consistent with the general symmetry requirements. As an example it is shown how the fundamental symmetries and the explicit chiral symmetry breaking pattern associated with the ENJL model are consistently preserved in this way.

Strongly coupled ’t Hooft model on the lattice

We study the strong coupling limit of the one-flavor and two-flavor massless 't Hooft models, $large-{\cal N}_c$-color $QCD_2$, on a lattice. We use staggered fermions and the Hamiltonian approach to lattice gauge theories. We show that the one-flavor model is effectively described by the antiferromagnetic Ising model, whose ground state is the vacuum of the gauge model in the infinite coupling limit; expanding around this ground state we derive a strong coupling expansion and compute the lowest lying hadron masses as well as the chiral condensate of the gauge theory. Our lattice computation well reproduces the results of the continuum theory. Baryons are massless in the infinite coupling limit; they acquire a mass already at the second order in the strong coupling expansion in agreement with the Witten argument that baryons are the $QCD$ solitons. The spectrum and chiral condensate of the two-flavor model are effectively described in terms of observables of the quantum antiferromagnetic Heisenberg model. We explicitly write the lowest lying hadron masses and chiral condensate in terms of spin-spin correlators on the ground state of the spin model. We show that the planar limit (${\cal N}_c\longrightarrow \infty$) of the gauge model corresponds to the large spin limit ($S\longrightarrow \infty$) of the antiferromagnet and compute the hadron mass spectrum in this limit finding that, also in this model, the pattern of chiral symmetry breaking of the continuum theory is well reproduced on the lattice.

Self-adjointness of the Two-Dimensional Massless Dirac Hamiltonian and Vacuum Polarization Effects in the Background of a Singular Magnetic Vortex

A massless spinor field is quantized in the background of a singular static magnetic vortex in 2+1-dimensional space-time. The method of self-adjoint extensions is employed to define the most general set of physically acceptable boundary conditions at the location of the vortex. Under these conditions, all effects of polarization of the massless fermionic vacuum in the vortex background are determined. Absence of anomaly is demonstrated, and patterns of both parity and chiral symmetry breaking are discussed.

The spectral density of the QCD Dirac operator and patterns of chiral symmetry breaking

We study the spectrum of the QCD Dirac operator for two colors with fermions in the fundamental representation and for two or more colors with adjoint fermions. For N f flavors, the chiral flavor symmetry of these theories is spontaneously broken according to SU (2 N f → Sp (2 N f ) and SU ( N f → O ( N f ), respectively, rather than the symmetry breaking pattern SU ( N f ) × SU ( N f ) → SU ( N f ) for QCD with three or more colors and fundamental fermions. In this paper we study the Dirac spectrum for the first two symmetry breaking patterns. Following previous work for the third case we find the Dirac spectrum in the domain λ ⪡ Λ QCD by means of partially quenched chiral perturbation theory. In particular, this result allows us to calculate the slope of the Dirac spectrum at λ = 0. We also show that for λ ⪡ 1/ L 2 Λ QCD (wing L the linear size fo the system) the Dirac spectrum is given by a chiral Random Matrix Theory with the symmetries of the Dirac operator.

Large- N c QCD and spontaneous chiral symmetry breaking

I report on recent work done in collaboration with Marc Knecht [1] on patterns of spontaneous chiral symmetry breaking in the large- N c limit of QCD-like theories, and with Santi Peris and Michel Perrottet [2] concerning the question of matching long and short distances in large- N c QCD.

Evidence for discrete chiral symmetry breaking in N=1 supersymmetric Yang-Mills theory

In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with dynamical gauginos we find evidence for two degenerate ground states at the supersymmetry point corresponding to zero gaugino mass. This is consistent with the expected pattern of spontaneous discrete chiral symmetry breaking Z 4→ Z 2 caused by gaugino condensation.

Chiral symmetry breaking and effective Lagrangians for softly broken supersymmetric QCD

We study supersymmetric QCD with N_f<N_c in the limit of small supersymmetry-breaking masses and smaller quark masses using the weak-coupling Kahler potential. We calculate the full spectrum of this theory, which manifests a chiral symmetry breaking pattern similar to that caused by the strong interactions of the standard model. We derive the chiral effective lagrangian for the pion degrees of freedom, and discuss the behavior in the formal limit of large squark and gluino masses and for large N_c. We show that the resulting scalings of the pion decay constant and pion masses in these limits differ from those expected in ordinary nonsupersymmetric QCD. Although there is no weak coupling expansion with N_f=N_c, we extend our results to this case by constructing a superfield quantum modified constraint in the presence of supersymmetry breaking.

SOFTLY BROKEN N=2 QCD WITH MASSIVE QUARK HYPERMULTIPLETS, II

We analyze the vacuum structure of N=2, SU(2) QCD with massive quark hypermultiplets, once supersymmetry is softly broken down to N=0 with dilaton and mass spurions. We give general expressions for the low energy couplings of the effective potential in terms of elliptic functions to have a complete numerical control of the model. We study in detail the possible phases of the theories with Nf=1,2 flavors for different values of the bare quark masses and the supersymmetry breaking parameters and we find a rich structure of first order phase transitions. The chiral symmetry breaking pattern of the Nf=2 theory is considered, and we obtain the pion Lagrangian for this model up to two derivatives. Exact expressions are given for the pion mass and Fπ in terms of the magnetic monopole description of chiral symmetry breaking.

Patterns of spontaneous chiral symmetry breaking in the large-Nc limit of QCD-like theories

It is shown that in vector-like gauge theories, such as QCD, and in the limit of a large number of colours Nc, the ordering pattern of narrow vector and axial-vector states at low energies is correlated with the size of the possible local order parameters of chiral symmetry breaking. This has implications on the underlying dynamics of spontaneous chiral symmetry breaking in QCD, and also on possible values of the parameter S for oblique electroweak corrections, the analogue of the QCD low energy constant L10.

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 ...

SOFTLY BROKEN N = 2 QCD

We analyze the possible soft breaking of (N = 2)-supersymmetric Yang–Mills theory with and without matter flavor preserving the analyticity properties of the Seiberg–Witten solution. For a small supersymmetry-breaking parameter with respect to the dynamical scale of the theory we obtain an exact expression for the effective potential. We describe in detail the onset of the confinement transition and some of the patterns of chiral symmetry breaking. If we extrapolate the results to the limit where supersymmetry decouples, we obtain hints indicating that perhaps a description of the QCD vacuum will require the use of Lagrangians containing simultaneously mutually nonlocal degrees of freedom (monopoles and dyons).

Phenomenology of a nonstandard Higgs boson in WLWL scattering.

In this paper we consider the phenomenology of a ``non-standard'' Higgs Boson in longitudinal gauge-Boson scattering. First, we present a composite Higgs model (based on an $SU(4)/Sp\,(4)$ chiral-symmetry breaking pattern) in which there is a non-standard Higgs Boson. Then we explore, in a model-independent way, the phenomenology of such a non-standard Higgs by calculating the chiral logarithmic corrections to longitudinal gauge scattering. This calculation is done using the Equivalence theorem and the Higgs is treated as a scalar-isoscalar resonance coupled to the Goldstone Bosons of the \mbox{$SU(2)_{L} \times SU(2)_{R}/SU(2)_{V}$} chiral symmetry breaking. We show that the most important deviation from the one Higgs-doublet standard model is parameterized by one unknown coefficient which is related to the Higgs width. The implications for future hadron colliders are discussed.

CHIRAL GAUGE E6 AS A BINDING GROUP FOR COMPOSITE LEPTONS, QUARKS AND HIGGS BOSONS

The uniqueness of the chiral gauge E6 symmetry in providing the mechanism of binding for composite models is stressed. A maximally symmetric pattern of chiral symmetry breaking, consistent with dynamical mass generation along with preservation of the strongly coupled E6 gauge symmetry, is considered. Chiral anomaly matching conditions for the residual chiral symmetry are studied and likely massless composite fermions are found. The possibility for these fermions as well as Goldstone bosons to be treated eventually as leptons, quarks and Higgs bosons is discussed. The scheme possesses the generic realistic-like features and could serve as a prototype for a realistic composite model.

Cabibbo mixing from strong-interaction condensates

In a scenario where the down and strange quark weak-interaction eigenstates are given a current mass, it is argued that a likely pattern of chiral symmetry breaking is one in which\(\left\langle {\bar uu} \right\rangle ,\left\langle {\bar dd} \right\rangle \) and\(\left\langle {\bar sd} \right\rangle = \left\langle {\bar ds} \right\rangle \) condensates form, the latter either instead of, or in addition to, an\(\left\langle {\bar ss} \right\rangle \) condensate. This results in a dynamical mixing contribution to the effectives-d mass matrix. Using previous estimates of quark mass ratios, the resulting Cabibbo angle is computed to be (13±4)°. A consistent solution is reached with zero Lagrangian mass for the up quark, providing a possible solution to the strongCP problem. In the absence of weak interactions,\(\left\langle {\bar sd} \right\rangle = \left\langle {\bar ds} \right\rangle = 0\), but\(\lim x \to \infty \left\langle {\bar s(x) d(x) \bar d(0) s(0)} \right\rangle \ne 0\), corresponding to a condensate of spatially noncorrelated\(\bar sd/\bar ds\) pairs, and plays a nearly identical role. Pauli-principle effects give this pair-condensed vacuum a lower energy than the usual spontaneously broken vacuum solution, and produces an allowed violation of cluster decomposition. Strangeness is not spontaneously broken, and no unwanted Goldstone bosons result.

Patterns of spontaneous chiral symmetry breaking

A model that exhibits two types of spontaneous chiral symmetry breaking belonging to the same chain, namely SU(2) L×SU(2) R→SU(2) V, is investigated. In addition to the conventional chiral symmetry breaking due to the q̄q condesation, a new phase induced by qq and q̄q̄ condensations, which generate a relativistic superconducting phase of the light fermion system, is shown to be realized. The superconducting phase is unstable against spontaneous separation of matter and anti-matter. The possibility of the existence of localized superconducting phases is compressed baryonic systems is discussed. The fermionic effects on the propagation of photon and gluons are investigated in the superconducting phase of the model.