Showing papers on "Chiral anomaly published in 2002"

Chiral Rings and Anomalies in Supersymmetric Gauge Theory

Abstract: Motivated by recent work of Dijkgraaf and Vafa, we study anomalies and the chiral ring structure in a supersymmetric U(N) gauge theory with an adjoint chiral superfield and an arbitrary superpotential. A certain generalization of the Konishi anomaly leads to an equation which is identical to the loop equation of a bosonic matrix model. This allows us to solve for the expectation values of the chiral operators as functions of a finite number of ``integration constants.'' From this, we can derive the Dijkgraaf-Vafa relation of the effective superpotential to a matrix model. Some of our results are applicable to more general theories. For example, we determine the classical relations and quantum deformations of the chiral ring of = 1 super Yang-Mills theory with SU(N) gauge group, showing, as one consequence, that all supersymmetric vacua of this theory have a nonzero chiral condensate.

Gravity dual of the chiral anomaly

Abstract: We study effects associated with the chiral anomaly for a cascading SU(N+ M)×SU(N) gauge theory using gauge/gravity duality. In the gravity dual the anomaly is a classical feature of the supergravity solution, and the breaking of the U(1) R-symmetry down to Z2M proceeds via the Higgs mechanism.

Holographic Renormalization and Ward Identities with the Hamilton-Jacobi Method

Abstract: A systematic procedure for performing holographic renormalization, which makes use of the Hamilton-Jacobi method, is proposed and applied to a bulk theory of gravity interacting with a scalar field and a U(1) gauge field in the Stueckelberg formalism. We describe how the power divergences are obtained as solutions of a set of "descent equations" stemming from the radial Hamiltonian constraint of the theory. In addition, we isolate the logarithmic divergences, which are closely related to anomalies. The method allows to determine also the exact one-point functions of the dual field theory. Using the other Hamiltonian constraints of the bulk theory, we derive the Ward identities for diffeomorphisms and gauge invariance. In particular, we demonstrate the breaking of U(1)_R current conservation, recovering the holographic chiral anomaly recently discussed in hep-th/0112119 and hep-th/0202056.

Non-perturbative Renormalisation of Domain Wall Fermions: Quark Bilinears

Abstract: We find the renormalisation coefficients of the quark field and t he flavour non-singlet fermion bilinear operators for the domain wall fermion action, in the regularisation independent (RI) renormalisation scheme. Our results are from a quenched simulation, on a 16 3 ×32 lattice, with � = 6.0 and an extent in the fifth dimension of 16. We also discuss the expected effects of the residual chiral symmetry breaking inherent in a domain wall fermion simulation with a finite fifth dimension, and study the evidence for both explicit and spontaneous chiral symmetry breaking effects in our numerical results. We find that the relations between different renormalisation factors predicted by chiral symmetry are, to a good approximation, satisfied by our results and that systematic effects due to the (low energy) spontaneous chiral symmetry breaking and zero-modes can be controlled. Our results are compared against the perturbative predictions for both their absolute value and renormalisation scale dependence.

Real-time pion propagation in finite-temperature QCD

Abstract: We argue that in QCD near the chiral limit, at all temperatures below the chiral phase transition, the dispersion relation of soft pions can be expressed entirely in terms of three temperature-dependent quantities: the pion screening mass, a pion decay constant, and the axial isospin susceptibility. The definitions of these quantities are given in terms of equal-time (static) correlation functions. Thus, all three quantities can be determined directly by lattice methods. The precise meaning of the Gell-Mann--Oakes--Renner relation at finite temperature is given.

Nicolai mapping versus exact chiral symmetry on the lattice

Abstract: The two-dimensional $N=2$ Wess-Zumino model is constructed on the lattice through Nicolai mapping with a Ginsparg-Wilson fermion. The Nicolai mapping requires a certain would-be surface term in the bosonic action which ensures the vacuum energy cancellation even on the lattice, but inevitably breaks chiral symmetry. With the Ginsparg-Wilson fermion, the holomorphic structure of the would-be surface term is maintained, leaving a discrete subgroup of the exact chiral symmetry intact for a monomial scalar potential. Through this feature both the boson and fermion can be kept massless on the lattice without any fine-tuning.

Exactly solvable matrix models for the dynamical generation of space-time in superstring theory

Abstract: We present a class of solvable SO(D) symmetric matrix models with D bosonic matrices coupled to chiral fermions. The SO(D) symmetry is spontaneously broken due to the phase of the fermion integral. This demonstrates the conjectured mechanism for the dynamical generation of four-dimensional space-time in the IIB matrix model, which was proposed as a nonperturbative definition of type IIB superstring theory in ten dimensions.

Chiral logs in the presence of staggered flavor symmetry breaking

Abstract: Chiral logarithms in ${m}_{\ensuremath{\pi}}^{2}$ are calculated at one loop, taking into account the leading contributions to flavor symmetry breaking due to staggered fermions. I treat both the full QCD case $(2+1$ light dynamical flavors) and the quenched case; finite volume corrections are included. My starting point is the effective chiral Lagrangian introduced by Lee and Sharpe. It is necessary to understand the one-loop diagrams in the ``quark flow'' picture in order to adjust the calculation to correspond to the desired number of dynamical quarks.

Does one observe chiral symmetry restoration in baryon spectrum

Abstract: It has recently been suggested that the parity doublet structure seen in the spectrum of highly excited baryons may be due to effective chiral symmetry restoration for these states. We review the recent developments in this field. We demonstrate with a simple quantum-mechanical example that it is a very natural property of quantum systems that a symmetry breaking effect which is important for the low-lying spectrum of the system, can become unimportant for the highly-lying states; the highly lying states reveal a multiplet structure of nearly degenerate states. Using the well established concepts of quark-hadron duality, asymptotic freedom in QCD and validity of the operator product expansion in QCD we show that the spectral densities obtained with the local currents that are connected to each other via chiral transformations, very high in the spectrum must coincide. Hence effects of spontaneous breaking of chiral symmetry in QCD vacuum that are crucially important for the low-lying spectra, become irrelevant for the highly-lying states. Then to the extent that identifiable hadronic resonances still exist in the continuum spectrum at high excitations this implies that the highly excited hadrons must fall into multiplets associated with the representations of the chiral group. We demonstrate that this is indeed the case for meson spectra in the large $N_c$ limit. All possible parity-chiral multiplets are classified for baryons and it is demonstrated that the existing data on highly excited $N$ and $\Delta$ states at masses of 2 GeV and higher is consistent with approximate chiral symmetry restoration. However new experimental studies are needed to achieve any definitive conclusions.

Electromagnetic corrections in the anomaly sector

Abstract: Chiral perturbation theory in the anomaly sector for Nf = 2 is extended to include dynamical photons, thereby allowing a complete treatment of isospin breaking. A minimal set of independent chiral lagrangian terms is determined and the divergence structure is worked out. There are contributions from irreducible and also from reducible one-loop graphs, a feature of ChPT at order larger than four. The generating functional is non anomalous at order e2p4, but not necessarily at higher order in e2. Practical applications to γπ→ππ and to the π0→2γ amplitudes are considered. In the latter case, a complete discussion of the corrections beyond current algebra is presented including quark mass as well as electromagnetic effects.

Localized fermions and anomaly inflow via deconstruction

Abstract: We study fermion localization in gauge theory space. We consider four-dimensional product gauge groups in which light chiral fermions transform under different gauge factors of the product group. This construction provides a suppression of higher dimensional operators. For example, it can be used to suppress dangerous proton decay operators. The anomalies associated with the light chiral fermions are compensated by Wess-Zumino terms, which in the continuum limit reproduce the five-dimensional Chern-Simons term.

Nucleons in Two-Flavor Partially-Quenched Chiral Perturbation Theory

Abstract: Properties of the proton and the neutron are explored in partially-quenched chiral perturbation theory with two non-degenerate light flavors. Masses, magnetic moments, matrix elements of isovector twist-2 operators and axial-vector currents are computed at the one-loop level in the chiral expansion.

Example of resonance saturation at one loop

Abstract: We argue that the large-${N}_{c}$ expansion of QCD can be used to treat a Lagrangian of resonances in a perturbative way. As an illustration of this we compute the ${L}_{10}$ coupling of the chiral Lagrangian by integrating out resonance fields at one loop. Given a Lagrangian and a renormalization scheme, this is how in principle one can answer in a concrete and unambiguous manner questions such as at what scale resonance saturation takes place.

Vector manifestation and fate of vector mesons in dense matter

Abstract: We describe in-medium properties of hadrons in dense matter near chiral restoration using a Wilsonian matching to QCD of an effective field theory with hidden local symmetry at the chiral cutoff $\Lambda$. We find that chiral symmetry is restored in vector manifestation a la Harada and Yamawaki at a critical matter density $n_c$. We express the critical density in terms of QCD correlators in dense matter at the matching scale. In a manner completely analogous to what happens at the critical $N_f^c$ and at the critical temperature $T^c$, the vector meson mass is found to vanish (in the chiral limit) at chiral restoration. This result provides a support for Brown-Rho scaling predicted a decade ago.

Deformed nuclei in a chiral model

Abstract: We investigate the deformation properties of atomic nuclei in a hadronic chiral ${\mathrm{SU}}_{\mathrm{flavor}}(3)$ model approach. The parameters are fitted to hadron mass properties and adjustments for spherical finite nuclei have been performed. Using these parameters the deformation of a series of light and heavy nuclei are obtained in a two-dimensional self-consistent calculation. In addition a case of superdeformation in a heavy nucleus is studied.

Thermal rho and sigma mesons from chiral symmetry and unitarity

Abstract: We study the temperature evolution of the rho and sigma mass and width, using a unitary chiral approach The one-loop pipi scattering amplitude in chiral perturbation theory at Tnot equal0 is unitarized via the inverse amplitude method Our results predict a clear increase with T of both the rho and sigma widths The masses decrease slightly for high T, while the rhopipi coupling increases The rho behavior seems to be favored by experimental results In the sigma case, it signals chiral symmetry restoration

Chiral symmetry restoration and the string picture of hadrons

Abstract: QCD string picture of highly excited hadrons very naturally explains parity doubling once the chiral symmetry is restored high in the spectrum. In particular, the spin-orbit and tensor interactions of quarks at the ends of the string, related to dynamics of the string, vanish. High in the spectrum there appears higher degree of degeneracy, namely parity doublets with different angular momentum cluster around energy of the string in the given quantum state.

Microscopic Correlation Functions for the QCD Dirac Operator with Chemical Potential

Abstract: A chiral random matrix model with complex eigenvalues is solved as an effective model for QCD with nonvanishing chemical potential. The new correlation functions derived from it are conjectured to predict the local fluctuations of complex Dirac operator eigenvalues at zero virtuality. The parameter measuring the non-Hermiticity of the random matrix is related to the chemical potential. In the phase with broken chiral symmetry all spectral correlations are calculated for finite matrix size N and in the large-N limit at weak and strong non-Hermiticity. The derivation uses the orthogonality of the Laguerre polynomials in the complex plane.

Allowed eta-decay modes and chiral symmetry

Abstract: Recently, the development of chiral perturbation theory has allowed the generation of rigorous low-energy theorems for various hadronic processes based only on the chiral invariance of the underlying QCD Lagrangian. Such techniques are highly developed and well-tested in the domain of pionic and kaonic reactions. In this note we point out that with the addition of a few additional and reasonable assumptions similar predictive power is available for processes involving the eta meson.

Chiral Lagrangians at finite density

Abstract: The effective SU(2) chiral Lagrangian with external sources is given in the presence of nonvanishing nucleon densities by calculating the in-medium contributions of the chiral pion-nucleon Lagrangian. As a by-product, a relativistic quantum field theory for Fermi many-particle systems at zero temperature is directly derived from relativistic quantum field theory with functional methods.

Calculation of the chiral Lagrangian coefficients from the underlying theory of QCD: A simple approach

Abstract: We calculate the coefficients in the chiral Lagrangian approximately from QCD based on a previous study of deriving the chiral Lagrangian from the first principles of QCD in which the chiral Lagrangian coefficients are defined in terms of certain Green's functions in QCD. We first show that, in the large-N-c limit, the anomaly part contributions to the coefficients are exactly cancelled by certain terms in the normal part contributions, and the final results of the coefficients only concern the remaining normal part contributions depending on QCD interactions. We then do the calculation in a simple approach with the approximations of taking the large-N-c limit, the leading order in dynamical perturbation theory, and the improved ladder approximation; thereby the relevant Green's functions are expressed in terms of the quark self-energy Sigma(p(2)). By solving the Schwinger-Dyson equation for Sigma(p(2)), we obtain the approximate QCD predicted coefficients and quark condensate which are consistent with the experimental values.