Sigma Model Research Articles

Toward a quantum simulation of nonlinear sigma models with a topological term

We determine the mass gap of a two-dimensional $\text{O}(3)$ nonlinear sigma model augmented with a topological $\ensuremath{\theta}$-term using tensor network and digital quantum algorithms. As proof of principle, we consider the example $\ensuremath{\theta}=\ensuremath{\pi}$ and study its critical behavior on a quantum simulator by examining the entanglement entropy of the ground state. We confirm that the quantum theory is massless in the strong-coupling regime, in agreement with analytical results. However, we also highlight the limitations of current quantum algorithms, designed for noisy intermediate-scale quantum devices, in the theory simulation at weak coupling. Finally, we compare the performance of our quantum algorithms to classical tensor network methods.

Integrable crosscaps in classical sigma models

We study the integrable boundaries and crosscaps of classical sigma models. We show that there exists a classical analog of the integrability condition and KT-relation of the boundary and crosscap states of quantum spin chains. We also classify the integrable crosscaps for various sigma models including examples which are relevant in the AdS/CFT correspondence at strong coupling.

Dynamic Transformation of Domain Walls in Chiral Ferrimagnets

The dynamics of domain walls in ferrimagnets in which spatial dynamics invariance is violated because of the presence of the chiral Dzyaloshinskii–Moriya interaction with energy linear in sublattice spin density gradients is investigated theoretically. Analysis is performed based on numerical integration of equations in the sigma model generalized to the case of a ferrimagnet near the sublattice spin compensation point. It is shown that in contrast to conventional or chiral ferromagnets, chiral ferrimagnets can exhibit effects of dynamic transformation of the domain wall structure with the formation of more complex walls with a nonmonotonic behavior of the spin density in a wall upon an increase in the wall velocity. These effects are possible in a quite narrow neighborhood of the compensation point, and the width of this region increases upon an increase in the Dzyaloshinskii–Moriya interaction constant.

Soft limits of the wavefunction in exceptional scalar theories

We study the structure of the flat space wavefunctional in scalar field theories with nonlinearly realized symmetries. These symmetries imply soft theorems that are satisfied by wavefunction coefficients in the limit where one of the external momenta is scaled to zero. After elucidating the structure of these soft theorems in the nonlinear sigma model, Dirac-Born-Infeld, and galileon scalar theories, we combine them with information about the singularity structure of the wavefunction to bootstrap the wavefunction coefficients of these theories. We further systematize this construction through two types of recursion relations: one that utilizes the flat space scattering amplitude plus minimal information about soft limits, and an alternative that does not require amplitude input, but does require subleading soft information.

A statistical field theory underlying the thermodynamics of Ricci flow and gravity

This paper proposes a statistical field theory of quantum reference frame underlying Perelman’s analogies between his formalism of the Ricci flow and the thermodynamics. The theory is based on a [Formula: see text] quantum nonlinear sigma model (NLSM), interpreted as a quantum reference frame system which a to-be-studied quantum system is relative to. The statistic physics and thermodynamics of the quantum frame fields is studied by the density matrix obtained by the Gaussian approximation quantization. The induced Ricci flow of the frame fields and the Ricci–DeTurck flow of the frame fields associated with the density matrix are deduced. In this framework, the diffeomorphism anomaly of the theory has a deep thermodynamic interpretation. The trace anomaly is related to a Shannon entropy in terms of the density matrix, which monotonically flows and achieves its maximal value at the flow limit, called the Gradient Shrinking Ricci Soliton (GSRS), corresponding to a thermal equilibrium state of spacetime. A relative Shannon entropy with respect to the maximal entropy gives a statistical interpretation to Perelman’s partition function, which is also monotonic and gives an analogous H-theorem to the statistical frame fields system. A temporal static three-space of a GSRS four-spacetime is also a GSRS in lower three-dimension, we find that it is in a thermal equilibrium state, and Perelman’s analogies between his formalism and the thermodynamics of the frame fields in equilibrium can be explicitly given in the framework. By extending the validity of the Equivalence Principle to the quantum level, the quantum reference frame fields theory at low energy gives an effective theory of gravity, a scale-dependent Einstein–Hilbert action plus a cosmological constant is recovered. As a possible underlying microscopic theory of the gravitational system, the theory is also applied to understand the thermodynamics of the Schwarzschild black hole.

Weyl invariance, non-compact duality and conformal higher-derivative sigma models

We study a system of n Abelian vector fields coupled to frac{1}{2} n(n+1) complex scalars parametrising the Hermitian symmetric space {textsf{Sp}}(2n, {mathbb {R}})/ {textsf{U}}(n). This model is Weyl invariant and possesses the maximal non-compact duality group {textsf{Sp}}(2n, {mathbb {R}}). Although both symmetries are anomalous in the quantum theory, they should be respected by the logarithmic divergent term (the “induced action”) of the effective action obtained by integrating out the vector fields. We compute this induced action and demonstrate its Weyl and {textsf{Sp}}(2n, {mathbb {R}}) invariance. The resulting conformal higher-derivative sigma -model on {textsf{Sp}}(2n, {mathbb {R}})/ {textsf{U}}(n) is generalised to the cases where the fields take their values in (i) an arbitrary Kähler space; and (ii) an arbitrary Riemannian manifold. In both cases, the sigma -model Lagrangian generates a Weyl anomaly satisfying the Wess–Zumino consistency condition.

Virtues of a symmetric-structure double copy

We demonstrate a physical motivation for extending color-dual or BCJ double-copy construction to include theories with kinematic numerators that obey the same algebraic relations as symmetric structure constants, d^{abc}=Tr[{T^a,T^b}T^c]. We verify that U(N) nonlinear sigma model (NLSM) pions, long known to be color-dual in terms of antisymmetric adjoint factors, f^{abc}, are also color-dual in the sense of symmetric color structures, d^{abc}, explicitly through six-point scattering. This reframing of NLSM pion amplitudes complements our compositional construction of d^{abc} color-dual higher derivative gauge operators. With adjoint and symmetric color-dual kinematics, we can span all four-point effective photon operators via a double-copy construction using amplitudes from physical theories. We further comment on a tension between locality and adjoint effective numerators, and the implications for spanning gravitational effective operators with non-adjoint kinematics.

Magnetic-field-dependent electric-charge transport in hadronic medium at finite temperature

Electric charge transport of hadronic matter at finite temperature and magnetic field is studied within the linear sigma model. Anisotropic transport coefficients associated with the charge transport are estimated both in the weak and strong regimes of the magnetic field using the transport theory approach. In a weakly magnetized medium, the magnetic field effects are incorporated through the Lorentz force term in the Boltzmann equation. Strong magnetic field puts further constraints on the motion of charged particles through Landau quantization. Magnetic field-dependent thermal relaxation time is obtained from interaction rates of hadrons with the S-matrix approach by considering the Landau level kinematics of the charged hadrons. Mean-field effects are embedded in the analysis through the temperature-dependent hadron masses. Further, the hadronic medium response to a time-varying external electric field is studied in weak and strong magnetic field regimes. It is seen that electromagnetic responses of the hadronic matter have a strong dependence on the mean-field effects, sigma mass, the strength of the external fields, and its evolution in the medium.

Renormalization of supersymmetric Lifshitz sigma models

We study the renormalization of an mathcal{N} = 1 supersymmetric Lifshitz sigma model in three dimensions. The sigma model exhibits worldvolume anisotropy in space and time around the high-energy z = 2 Lifshitz point, such that the worldvolume is endowed with a foliation structure along a preferred time direction. In curved backgrounds, the target-space geometry is equipped with two distinct metrics, and the interacting sigma model is power-counting renormalizable. At low energies, the theory naturally flows toward the relativistic sigma model where Lorentz symmetry emerges. In the superspace formalism, we develop a heat kernel method that is covariantized with respect to the bimetric target-space geometry, using which we evaluate the one-loop beta-functions of the Lifshitz sigma model. This study forms an essential step toward a thorough understanding of the quantum critical supermembrane as a candidate high-energy completion of the relativistic supermembrane.

Probing the hadron mass spectrum in dense two-color QCD with the linear sigma model

We investigate modifications of hadron masses at finite quark chemical potential in two-flavor and two-color QCD, data of which are available from lattice simulations, within a linear sigma model based on approximate Pauli-Gursey $SU(4)$ symmetry. The model describes not only ground-state scalar diquarks and pseudoscalar mesons but also the excited pseudoscalar diquarks and scalar mesons; each ground-state diquark (meson) has the corresponding excited diquark (hadron) with opposite parity as a chiral partner. Effects of chiral symmetry breaking and diquark condensates are incorporated by a mean-field treatment. We show that various mixings among the hadrons, which are triggered by the breakdown of baryon number conservation in the superfluid phase, lead to a rich hadron mass spectrum. We discuss the influence of $U(1{)}_{A}$ anomaly on the density dependence of the mass spectrum and also manifestations of the chiral partner structures as the density increases in the superfluid phase. The predicted hadron masses are expected to provide future lattice simulations with useful information on such symmetry properties in dense two-color QCD.

Soft scalars and the geometry of the space of celestial conformal field theories

Known examples of the holographic dictionary in asymptotically anti--de Sitter spacetimes equate moduli spaces of bulk vacua with conformal manifolds in the dual quantum field theory. We demonstrate that the same identification holds for gravity in asymptotically flat spacetimes in any dimension, in accord with expectations derived from the celestial conformal field theory (CCFT) formalism. Soft limits of moduli scalars described by the sigma model are universal, and relate to parallel transport of $S$-matrix observables over the moduli space of bulk vacua. The leading ``soft moduli operator'' is the shadow transform of a dimension $\mathrm{\ensuremath{\Delta}}=d$ marginal operator $M(x)$. The universal form of the soft limit guarantees that $M(x)$ acts as a marginal deformation in the ${\mathrm{CCFT}}_{d}$, and coherent states of the soft scalars correspond to finite deformations along the conformal manifold. This manifold typically has curvature, which is captured by the antisymmetric double-soft theorem and which reflects the Berry curvature in ${\mathrm{CCFT}}_{d}$. We also compute the Mellin-transformed four-point function in the sigma model and compare to a formula of Kutasov for the curvature of the conformal manifold.

Inverse mass ordering of light scalar mesons in the Nambu–Jona-Lasinio model

AbstractThe masses of the low-lying scalar mesons are investigated in the three-flavor Nambu–Jona-Lasinio (NJL) model by treating the scalar mesons as composite objects of a quark and an antiquark. It is known that a simple $\bar{q}q$ picture fails to reproduce the so-called inverse mass ordering for the scalar mesons. Recently a new mechanism to reproduce the observed mass spectrum of the scalar mesons was proposed in a linear sigma model by introducing flavor symmetry breaking induced by the U(1) axial anomaly. Motivated by this proposal, we examine whether this new mechanism also works in the NJL model. By calculating the scalar meson masses, we find that the NJL model reproduces the observed mass ordering with sufficient strength of the new term. With this mechanism, it turns out that the constituent strange quark mass becomes degenerate to that of the up and down quarks if the inverse mass ordering is reproduced. We also discuss the scalar diquark masses to check the consistency of the degeneracy of the constituent quark masses with the light baryon masses.

Scale-dependent theory of the disordered electron liquid

We review the scaling theory of disordered itinerant electrons with e−e interactions. We first show how to adjust the microscopic Fermi-liquid theory to the presence of disorder. Then we describe the non-linear sigma model (NLSM) with interactions (Finkel’stein’s model). This model is closely connected to the Fermi liquid, but is more generally applicable, since it can also be viewed as a minimal effective functional describing disordered interacting electrons. Our discussion emphasizes the general structure of the theory, and the connection of the scaling parameters to conservation laws. We then move on to discuss the metal–insulator transition (MIT) in the disordered electron liquid in two and three dimensions. Generally speaking, this MIT is a non-trivial example of a quantum phase transition. The NLSM approach allows to identify the dynamical exponent connecting the spatial and energy scales, which is central for the description of the kinetic and thermodynamic behavior of the system in the critical region of the MIT in three dimensions. In two dimensions, the system can be discussed in terms of a flow in the disorder-interaction phase plane, which is controlled by a fixed point. We demonstrate that the two-parameter RG-equations accurately describe electrons in Si-MOSFETs including the observed non-monotonic behavior of the resistance and its strong drop at low temperatures. The theory can also be applied to systems with an attractive interaction in the Cooper channel, where it describes the suppression of superconductivity in disordered amorphous films. We extend our discussion to heat transport in the two-dimensional electron liquid. Similar to the electric conductivity, the thermal conductivity also acquires logarithmic corrections induced by the interplay of the electron interaction and disorder. The resulting thermal conductivity can be calculated in the NLSM formalism after introducing so-called gravitational potentials. It may be concluded that the combined effect of disorder and e−e interactions determines all aspects of the physics of itinerant electrons in the presence of disorder.

Holographic duals of N=1 quivers in 5d and their nonrelativistic limits

We explore nonrelativistic limits of $\mathcal{N}=1$ quiver gauge theories in 5d. The stringy counterpart of these Super Conformal Field Theories (SCFTs) is characterized by torsional string Newton-Cartan (TSNC) sigma models which are defined over non-Lorentzian manifolds. We further show that under transverse T duality, these TSNC sigma models are mapped into another new class of nonrelativistic sigma models which are defined over a T-dual TSNC background. Considering nonrelativistic limits of various field theory observables in a holographic setup, we further estimate corresponding entities in the TSNC limit of $\mathcal{N}=1$ quivers. We carry out a parallel analysis on holomorphic functions and the associated pole structures in the nonrelativistic limit of ($p$, $q$) five brane webs. In particular, we investigate the generic structure of various loop operators in a nonrelativistic setup and explore their properties under S duality. Finally, we comment on the large $c$ limit of Ramond-Ramond (RR) fields and discuss the associated S-duality transformation rules in the nonrelativistic limit of $\mathcal{N}=1$ quivers.

Analysis of supply chain management system using lean six sigma: Balanced scoredcard parameters approach

The potential development of the beauty product industry in Indonesia is considered very attractive. The beauty products industry and trade in Indonesia is projected to increase by USD 7.5 billion with a growth of 6.5% annually for the next five years. The huge potential in the cosmetics retail business is considered to trigger the emergence of competition, especially in the supply chain system which has implications for product affordability to consumers. So that this becomes an interesting condition for research to be carried out as well as efforts to provide certain improvement treatments so that there is an improvement in the flow of the supply system in the object company. In this study, 3 layers of the research process will be carried out, namely observing and describing the existing supply chain system in the research object company, improving and treating the supply chain system using a lean six sigma model with stages of define, measure, analyze, improve, control (DMAIC), and make observations as well as measure the results of improvement using 4 (four) balanced scoredcard performance indicators. Data mining using observation methods, interviews, scoring key performance indicators in each perspective, and study of company operational administration data. Based on the results of study, the supply system based on 4 balanced scoredcard indicators still has shortcomings, namely in the value of debt-to-equity ratio, quantity and customer quality, internal business organization, and personnel accountability. The recommendation is that this study can have an improving effect on the object company and also be a reference for other companies specifically with the same segmentation.

Application of a six sigma model to evaluate the analytical performance of cerebrospinal fluid biochemical analytes and the design of quality control strategies for these assays: A single-centre study

BackgroundIn this study, we applied a six sigma model to examine cerebrospinal fluid (CSF) biochemical analytes for the first time. Our goal was to evaluate the analytical performance of various CSF biochemical analytes, design an optimized internal quality control (IQC) strategy, and formulate scientific and reasonable improvement plans. MethodsThe sigma values of CSF total protein (CSF-TP), albumin (CSF-ALB), chloride (CSF-Cl), and glucose (CSF-GLU) were calculated using the following formula: sigma = [TEa(%)−|bias(%)|]/CV(%). The analytical performance of each analyte was shown using a normalized sigma method decision chart. Individualized IQC schemes and improvement protocols for CSF biochemical analytes were formulated using the Westgard sigma rule flow chart with batch size and quality goal index (QGI). ResultsThe distribution of sigma values for CSF biochemical analytes ranged from 5.0 to 9.9, and the sigma values varied for different concentrations of the same analyte. The analytical performance of the CSF assays at the two QC levels is displayed visually in normalized sigma method decision charts. Individualized IQC strategies for CSF biochemical analytes were as follows: for CSF-ALB, CSF-TP and CSF-Cl, use 13s with N = 2 and R = 1000; for CSF-GLU, use 13s/22s/R4s with N = 2 and R = 450. In addition, priority improvement measures for analytes with sigma values less than 6 (CSF-GLU) were formulated based on the QGI, and their analytical performance was improved after the corresponding improvement measures were taken. ConclusionsThe six sigma model has significant advantages in practical applications involving CSF biochemical analytes and is highly useful for quality assurance and quality improvement.

Logarithmic corrections to O(a) and O(a^2) effects in lattice QCD with Wilson or Ginsparg–Wilson quarks

We derive the asymptotic lattice spacing dependence a^n[2b_0bar{g}^2(1/a)]^{hat{Gamma }_i} relevant for spectral quantities of lattice QCD, when using Wilson, textrm{O}(a) improved Wilson or Ginsparg–Wilson quarks. We give some examples for the spectra encountered for hat{Gamma }_i including the partially quenched case, mixed actions and using two different discretisations for dynamical quarks. This also includes maximally twisted mass QCD relying on automatic textrm{O}(a) improvement. At textrm{O}(a^2), all cases considered have min _ihat{Gamma }_igtrsim -0.3 if N_{textrm{f}}le 4, which ensures that the leading order lattice artifacts are not severely logarithmically enhanced in contrast to the O(3) non-linear sigma model (Balog et al. in Nucl Phys B 824:563–615, 2010; Balog et al. in Phys Lett B 676:188–192, 2009). However, we find a very dense spectrum of these leading powers, which may result in major pile-ups and cancellations. We present in detail the computational strategy employed to obtain the 1-loop anomalous dimensions already used in Husung et al. (Phys Lett B 829:137069, 2022).

Anderson localization at the boundary of a two-dimensional topological superconductor

A one-dimensional boundary of a two-dimensional topological superconductor can host a number of topologically protected chiral modes. Combining two topological superconductors with different topological indices, it is possible to achieve a situation when only a given number of channels ($m$) are topologically protected, while others are not and therefore are subject to Anderson localization in the presence of disorder. We study transport properties of such quasi-one-dimensional quantum wires with broken time-reversal and spin-rotational symmetries (class D) and calculate the average conductance, its variance and the third cumulant, as well as the average shot noise power. The results are obtained for arbitrary wire length, tracing a crossover from the diffusive Drude regime to the regime of strong localization where only $m$ protected channels conduct. Our approach is based on the nonperturbative treatment of the nonlinear supersymmetric sigma model of symmetry class D with two replicas developed in our recent publication [D. S. Antonenko et al., Phys. Rev. B 102, 195152 (2020)]. The presence of topologically protected modes results in the appearance of a topological Wess-Zumino-Witten term in the sigma-model action, which leads to an additional subsidiary series of eigenstates of the transfer-matrix Hamiltonian. The developed formalism can be applied to study the interplay of Anderson localization and topological protection in quantum wires of other symmetry classes.

The fate of discrete torsion on resolved heterotic [formula omitted] orbifolds using (0,2) GLSMs

This paper aims to shed light on what becomes of discrete torsion within heterotic orbifolds when they are resolved to smooth geometries. Gauged Linear Sigma Models (GLSMs) possessing (0,2) worldsheet supersymmetry are employed as interpolations between them. This question is addressed for resolutions of the non–compact C3/Z2×Z2 and the compact T6/Z2×Z2 orbifolds to keep track of local and global aspects. The GLSMs associated with the non–compact orbifold with or without torsion are to a large extent equivalent: only when expressed in the same superfield basis, a field redefinition anomaly arises among them, which in the orbifold limit reproduces the discrete torsion phases. Previously unknown, novel resolution GLSMs for T6/Z2×Z2 are constructed. The GLSM associated with the torsional compact orbifold suffers from mixed gauge anomalies, which need to be cancelled by appropriate logarithmic superfield dependent FI–terms on the worldsheet, signalling H–flux due to NS5–branes supported at the exceptional cycles.

Grothendieck’s dessins d’enfants in a web of dualities. III

We give a new proof of the equivalence between the dessin partition function and the partition function of the Laguerre unitary ensemble (LUE), originally found by Ambjørn and Chekhov. We also introduce a correction factor for the dessin/LUE partition function, and show that the corrected dessin/LUE partition function is a Dubrovin–Zhang type tau-function of the Toda lattice hierarchy. As an application, we use the approach of Dubrovin and Zhang for the computation of the dessin correlators. In physicists’ terminology, we establish dualities among dessin counting, generalized Penner model, and -topological sigma model.