Chiral Sigma Model Research Articles

Gravity from holomorphic discs and celestial Lw1+∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Lw_{1+\\infty }$$\\end{document} symmetries

The study of physical theories in various signatures has been important for uncovering structures not easily visible or definable in Lorentz signature. In split signature, global twistor constructions for conformally self-dual (SD) gravity and Yang–Mills construct solutions from twistor data that can be expressed in terms of free data without gauge freedom. This is developed for asymptotically flat SD gravity to give a fully nonlinear encoding of the asymptotic gravitational data in terms of a real homogeneous generating function h on the real twistor space. The recently discovered Lw1+∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Lw_{1+\\infty }$$\\end{document} celestial symmetries, when real, act locally as passive Poisson diffeomorphisms on the real twistor space. The twistor data, h, generates an imaginary such Poisson transformation that then generates the gravitational field by shifting the real slice of the twistor space. The twistor chiral sigma models, whose correlators yield the Einstein gravity tree-level S-matrix, are reformulated as theories of holomorphic discs in twistor space whose boundaries lie on the deformed real slice determined by h. The real Lw1+∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Lw_{1+\\infty }$$\\end{document} symmetries act on the corresponding formula for the S-matrix geometrically with vanishing Noether currents, but imaginary generators yield graviton vertex operators that generate gravitons in the perturbative expansion. A generating function for the all plus 1-loop amplitude, the analogous framework for Yang–Mills, possible interpretations in Lorentz signature and similar open string formulations of twistor and ambitwistor strings in 4d in split signature, are briefly discussed.

Spontaneous scalarization in proto-neutron stars

Proto-neutron stars are born when a highly evolved and massive star collapses under gravity. In this paper, we investigate the spontaneous scalarization in proto-neutron stars. Based on the scalar tensor theory of gravity as well as the physical conditions in proto-neutron star, we examine the structure of proto-neutron star. To describe the fluid in proto-neutron star, we utilize SU(2) chiral sigma model and the finite temperature extension of the Brueckner–Bethe–Goldstone quantum many-body theory in the Brueckner–Hartree–Fock approximation. Here, we apply the equation of state of proto-neutron stars considering different cases i.e. hot pure neutron matter and hot beta -stable neutron star matter without neutrino trapping as well as with neutrino trapping. The effects of temperature and entropy of proto-neutron stars on the star structure are also studied. Our results confirm that the spontaneous scalarization is affected by different physical conditions in proto-neutron stars.

Influence of the equation of state on a compact star made of hidden-sector nucleons

Abstract We study a compact star made of degenerate hidden-sector nucleons which will be a candidate for cold dark matter. A hidden sector like quantum chromodynamics is considered, and as the low-energy effective theory we take the (hidden-sector) $ SU(2) $ chiral sigma model including a hidden-sector vector meson. With the mean field approximation, we find that one can treat the equation of state (EOS) of our model analytically by introducing a variable which depends on the Fermi momentum. The EOS is specified by the two parameters $ C'_{\sigma} $, $ C'_{\omega} $, and we discuss how these parameters affect the mass–radius relation for a compact star as well as the EOS. The dependence of the maximum stable mass of compact stars on the parameter $ C'_{\sigma} $ will also be discussed.

Chiral strings, topological branes, and a generalised Weyl-invariance

We introduce a sigma model Lagrangian generalising a number of new and old models which can be thought of as chiral, including the Schild string, ambitwistor strings, and the recently introduced tensionless AdS twistor strings. This “chiral sigma model” describes maps from a [Formula: see text]-brane worldvolume into a symplectic space and is manifestly invariant under diffeomorphisms as well as under a “generalised Weyl invariance” acting on space–time coordinates and worldvolume fields simultaneously. Construction of the Batalin–Vilkovisky master action leads to a BRST operator under which the gauge-fixed action is BRST-exact; we discuss whether this implies that the chiral brane sigma model defines a topological field theory.

Universal coefficient of the exact correlator of a large-Nmatrix field theory

Exact expressions have been proposed for correlation functions of the large-$N$ (planar) limit of the $(1+1)$-dimensional ${\rm SU}(N)\times {\rm SU}(N)$ principal chiral sigma model. These were obtained with the form-factor bootstrap. The short-distance form of the two-point function of the scaling field $\Phi(x)$, was found to be $N^{-1}\langle {\rm Tr}\,\Phi(0)^{\dagger} \Phi(x)\rangle=C_{2}\ln^{2}mx$, where $m$ is the mass gap, in agreement with the perturbative renormalization group. Here we point out that the universal coefficient $C_{2}$, is proportional to the mean first-passage time of a L\'{e}vy flight in one dimension. This observation enables us to calculate $C_{2}=1/16\pi$.

Confinement-Higgs phase crossover as a lattice artifact in 1 + 1 dimensions

We examine the phase structure of massive Yang-Mills theory in 1+1 dimensions. This theory is equivalent to a gauged principal chiral sigma model. It has been previously shown that the gauged theory has only a confined phase, and no Higgs phase in the continuum, and at infinite volume. There are no massive gluons, but only hadron-like bound states of sigma-model particles. The reason is that the gluon mass diverges, being proportional to the two-point correlation function of the renormalized field of the sigma model at $x=0$. We use exact large-$N$ results to show that after introducing a lattice regularization and typical values of the coupling constants used in Monte Carlo simulations, the gluon mass becomes finite, and even sometimes small. A smooth crossover into a Higgs phase can then appear. For small volumes and large $N$, we find an analytic expression for the gluon mass, which depends on the coupling constants and the volume. We argue that this Higgs phase is qualitatively similar to the one observed in lattice computations at $N=2$.

Nontrivial thermodynamics in ’t Hooft’s large-Nlimit

We study the finite volume/temperature correlation functions of the (1+1)-dimensional ${\rm SU}(N)$ principal chiral sigma model in the planar limit. The exact S-matrix of the sigma model is known to simplify drastically at large $N$, and this leads to trivial thermodynamic Bethe ansatz (TBA) equations. The partition function, if derived using the TBA, can be shown to be that of free particles. We show that the correlation functions and expectation values of operators at finite volume/temperature are not those of the free theory, and that the TBA does not give enough information to calculate them. Our analysis is done using the Leclair-Mussardo formula for finite-volume correlators, and knowledge of the exact infinite-volume form factors. We present analytical results for the one-point function of the energy-momentum tensor, and the two-point function of the renormalized field operator. The results for the energy-momentum tensor can be used to define a nontrivial partition function.

U(2)A×U(2)V-symmetric fixed point from the functional renormalization group

The existence of an U(2)xU(2)-symmetric fixed point in the chiral linear sigma model is confirmed using the Functional Renormalization Group (FRG). Its stability properties and the implications for the order of the chiral phase transition of two-flavor quantum chromodynamics (QCD) are discussed. Furthermore, several technical conclusions are drawn from the comparison with the results of resummed loop expansions.

Seeing asymptotic freedom in an exact correlator of a large-Nmatrix field theory

Exact expressions for correlation functions are known for the large-$N$ (planar) limit of the $(1+1)$-dimensional ${\rm SU}(N)\times {\rm SU}(N)$ principal chiral sigma model. These were obtained with the form-factor bootstrap, an entirely nonperturbative method. The large-$N$ solution of this asymptotically-free model is far less trivial than that of O($N$) sigma model (or other isovector models). Here we study the Euclidean two-point correlation function $N^{-1}< {\rm Tr}\,\Phi(0)^{\dagger} \Phi(x)>$, where $\Phi(x)\sim Z^{-1/2}U(x)$ is the scaling field and $U(x)\in SU(N)$ is the bare field. We express the two-point function in terms of the spectrum of the operator $\sqrt{-d^{2}/du^{2}}$, where $u\in (-1,1)$. At short distances, this expression perfectly matches the result from the perturbative renormalization group.

Two-parameter scaling theory of transport near a spectral node

We investigate the finite-size scaling behavior of the conductivity in a two-dimensional Dirac electron gas within a chiral sigma model. Based on the fact that the conductivity is a function of system size times scattering rate, we obtain a two-parameter scaling flow toward a finite fixed point. The latter is the minimal conductivity of the infinite system. Depending on boundary conditions, we also observe unstable fixed points with conductivities much larger than the experimentally observed values, which may account for results found in some numerical simulations. By including a spectral gap we extend our scaling approach to describe a metal-insulator transition.

Chiral logarithmic sigma model at finite temperature and baryonic chemical potential

A logarithmic potential is suggested to study the chiral phase transition, the critical temperature, and the meson masses at finite temperature and baryonic chemical potential. The logarithmic potential is based on some aspects of quantum chromodynamics (QCD) theory. The model has been solved in the mean-field approximation. We found that the behavior of meson masses takes a similar behavior as in the original sigma model and the Nambu–Jona-Lasinio model. The critical temperature is reduced in comparison with the original sigma model and it is in good agreement with recent lattice QCD results. The chiral phase transition is crossover in the case of chiral explicit breaking symmetry. The Goldstone boson theorem is studied, in which the meson mass is massive and pion mass is massless at lower temperatures. Our conclusions indicate to the present model successfully predicts the phase transition as well as in the original quark sigma model and the Nambu–Jona–Lasinio model. A new advantage of the present model, the critical temperature is in good agreement with lattice QCD results at zero chemical potential. A condition of spontaneous breaking symmetry is necessary to satisfy the Goldstone theorem in the chiral limit.

(2+1)-dimensional Yang-Mills theory and form factor perturbation theory

We study Yang Mills theory in $2+1$ dimensions, as an array of coupled ($1+1$)-dimensional principal chiral sigma models. This can be understood as an anisotropic limit where one of the space-time dimensions is discrete and the others are continuous. The $SU(N)\ifmmode\times\else\texttimes\fi{}SU(N)$ principal chiral sigma model in $1+1$ dimensions is integrable, asymptotically free and has massive excitations. New exact form factors and correlation functions of the sigma model have recently been found by the author and P. Orland. In this paper, we use these new results to calculate physical quantities in ($2+1$)-dimensional Yang-Mills theory, generalizing previous $SU(2)$ results by Orland, which include the string tensions and the low-lying glueball spectrum. We also present a new approach to calculate two-point correlation functions of operators using the light glueball states. The anisotropy of the theory yields different correlation functions for operators separated in the ${x}^{1}$ and ${x}^{2}$ directions.

Dynamical mass reduction in the massive Yang-Mills spectrum in1+1dimensions

The (1+1)-dimensional SU}(N) Yang-Mills Lagrangian, with bare mass M, and gauge coupling e, naively describes gluons of mass M. In fact, renormalization forces M to infinity. The system is in a confined phase, instead of a Higgs phase. The spectrum of this diverging-bare-mass theory contains particles of finite mass. There are an infinite number of physical particles, which are confined hadron-like bound states of fundamental colored excitations. These particles transform under irreducible representations of the global subgroup of the explicitly-broken gauge symmetry. The fundamental excitations are those of the SU(N) X SU(N) principal chiral sigma model, with coupling e/M. We find the masses of meson-like bound states of two elementary excitations. This is done using the exact S matrix of the sigma model. We point out that the color-singlet spectrum coincides with that of the weakly-coupled anisotropic SU(N) gauge theory in 2+1 dimensions. We also briefly comment on how the spectrum behaves in the 't Hooft limit, with N approaching infinity.

What has been discovered at 125 GeV by the CMS and the ATLAS experiments?

While looking for the putative Higgs boson of the Standard Model of particle physics, recently, the CMS and the ATLAS experiments at CERN have found strong signals of a new particle at about 125GeV. However in July 2012 the decay channels of this particle had some unexpected and puzzling anomalies not explainable by the Standard Model. By March 2013 they had seen these signals at about well less than 3\( \sigma\) confidence level. It is expected that the final definitive analysis shall still take quite some time. Here we show that what they may have found at 125GeV is the long sought for and missing ingredient of the strong interaction: the sigma-meson of the Chiral Sigma Model, within the framework of the Skyrme model with a topological interpretation of the baryons. Just like a massless gauge boson is a requirement, and hence a prediction of the local gauge theories, in the the same manner, a very heavy scalar meson is a requirement and hence a prediction of the Skyrme model of the hadrons. The 125GeV particle discovered by the CMS and the ATLAS groups may be an experimental confirmation of this unique prediction of the topological Skyrme model. However the bottom line is that even if the experimentalists finally confirm that this 125GeV entity is the expected Higgs boson, then there still remains to discover another heavier scalar particle as the sigma-meson of the chiral sigma model/Skyrme model, which remains its unique prediction, as shown in this paper.

Summing planar diagrams by an integrable bootstrap. II

We continue our investigation of correlation functions of the large-N (planar) limit of the (1+1)-dimensional principal chiral sigma model, whose bare field U(x) lies in the fundamental matrix representation of SU(N). We find all the form factors of the renormalized field. An exact formula for Wightman and time-ordered correlation functions is found.

Strange mass dependence of the tricritical point in theU(3)L×U(3)Rchiral sigma model

We study the strange quark mass dependence of the tricritical point of the $U(3{)}_{L}\ifmmode\times\else\texttimes\fi{}U(3{)}_{R}$ linear sigma model in the chiral limit. Assuming that the tricritical point is at a large strange mass value, the strange sector as well as the $\ensuremath{\eta}\ensuremath{-}{a}_{0}$ sector decouples from the light degrees of freedom which determines the thermodynamics. By tracing this decoupling we arrive from the original $U(3{)}_{L}\ifmmode\times\else\texttimes\fi{}U(3{)}_{R}$ symmetric model, going through the $U(2{)}_{L}\ifmmode\times\else\texttimes\fi{}U(2{)}_{R}$ symmetric one, at the $SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{R}$ linear sigma model. One-loop level beta functions for the running of the parameters in each of these models and tree-level matching of the coupling of these models performed at intermediate scales are used to determine the influence of the heavy sector on the parameters of the $SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{R}$ linear sigma model. By investigating the thermodynamics of this latter model we identified the tricritical surface of the $U(3{)}_{L}\ifmmode\times\else\texttimes\fi{}U(3{)}_{R}$ linear sigma model in the chiral limit. To apply the results for QCD we used different scenarios for the ${m}_{s}$ and ${\ensuremath{\mu}}_{q}$ dependence of the effective model parameters, and then the ${\ensuremath{\mu}}_{q}^{\mathrm{TCP}}({m}_{s})$ function can be determined. Depending on the details, a curve bending upwards or downwards near ${\ensuremath{\mu}}_{q}=0$ can be obtained, while with explicit chemical potential dependence of the parameters the direction of the curve can change with ${m}_{s}$, too.

Kac–Moody and Virasoro symmetries of principal chiral sigma models

It is commonly asserted that there is a G ˆ × G centreless Kac–Moody extension of the manifest G × G global symmetry of the two-dimensional principal chiral model (PCM) for the group manifold G. Here, we show that the symmetry is in fact larger, namely G ˆ × G ˆ , the full centreless Kac–Moody extension of the entire manifest G × G global symmetry. Extending previous results in the literature, we also obtain an explicit realisation of the Virasoro-like symmetry of the PCM, generated by K n = L n + 1 − L n − 1 for both positive and negative n. We show that these generators obey Sugawara-type commutation relations with the two commuting copies of the Kac–Moody algebra G ˆ .

Extended relativistic chiral mean field model for nuclear matter

We study nuclear matter properties based on the chiral sigma model. We formulate the extended relativistic chiral mean-field model by using the tensor optimized shell-model prescription developed for the description of the tensor interaction in finite nuclei. We apply further the unitary correlation operator model prescription to the treatment of the short-range repulsion in the pion channel. The remaining effects are treated phenomenologically in terms of the \ensuremath{\omega}-meson coupling term in the relativistic mean-field approximation. We discuss the equation of state and the chiral properties of nuclear matter.

CHIRAL SYMMETRY IN NUCLEAR MANY BODY SYSTEM

The pion was introduced by Yukawa as the mediator of nucleon-nucleon interaction to bind nucleons in nucleus. Due to its characteristic properties, however, the pion had not be used until recent years for description of nuclei. We present here a newly developed method to treat the pion exchange interaction in nuclei. We study nuclear structure by using the chiral sigma model lagrangian in the relativistic chiral mean field model with projection. The pion develops mean field and provides a magic number effect. We demonstrate also the ability of treating tensor interaction due to pion exchange in terms of tensor optimized shell model.

Quasifermion spectrum at finite temperature from coupled Schwinger-Dyson equations for a fermion-boson system

We nonperturbatively investigate a fermion spectrum at finite temperature in a chiral invariant linear sigma model. Coupled Schwinger-Dyson equations for fermion and boson are developed in the real time formalism and solved numerically. From the coupling of a massless fermion with a massive boson, the fermion spectrum shows a three-peak structure at some temperatures even for the strong coupling region. This means that the three-peak structure which was originally found in the one-loop calculation is stable against higher order corrections even in the strong coupling region.