Sigma Model Research Articles

QCD Phase Structure and In-Medium Modifications of Meson Masses in Polyakov Linear-Sigma Model with Finite Isospin Asymmetry

In the QCD-like effective model, the Polyakov linear-sigma model, the isospin sigma field (σ¯3=fK±−fK0) and the third generator of the matrix of the explicit symmetry breaking [h3=ma02fK±−fK0] are estimated in terms of the decay constants of the neutral (fK0) and charged Kaon (fK±) and the mass of a0 meson. Both quantities σ¯3 and h3 are then evaluated, at finite baryon (μB), isospin chemical potential (μI), and temperature (T). Thereby, the dependence of the critical temperature on isospin chemical potential could be mapped out in the (T−μI) phase diagram In the QCD-like effective model, the Polyakov linear-sigma model, the isospin sigma field (σ¯3=fK±−fK0) and the third generator of the matrix of the explicit symmetry breaking [h3=ma02fK±−fK0] are estimated in terms of the decay constants of the neutral (fK0) and charged Kaon (fK±) and the mass of a0 meson. Both quantities σ¯3 and h3 are then evaluated, at finite baryon (μB), isospin chemical potential (μI), and temperature (T). Thereby, the dependence of the critical temperature on isospin chemical potential could be mapped out in the (T−μI) phase diagram. The in-medium modifications of pseudoscalars (Jpc=0−+), scalars (Jpc=0++), vectors (Jpc=1−−), and axial-vectors (Jpc=1++) meson states are then analyzed in thermal and dense medium. We conclude that the QCD phase diagram (T−μI) is qualitatively similar to the (T−μB) phase diagram. We also conclude that both temperature and isospin chemical potential enhance the in-medium modifications of the meson states a0, σ, η′, π, f0, κ, η, K, ρ, ω, κ*, ϕ, a1, f1, K*, and f1*. Regarding their chemical potential, at high temperatures the various meson states likely dissolve into colored partonic phase. In this limit, the meson masses form a universal bundle. Thus, we conclude that the increase in the chemical potential similar to temperature derives the colorless confined meson states into the colored deconfined parton phase.

Renormalon subtraction in OPE by dual space approach: nonlinear sigma model and QCD

It is becoming more important to subtract renormalons efficiently from perturbative calculations, in order to achieve high precision QCD calculations. We propose a new framework “Dual Space Approach” for renormalon separation, which enables subtraction of multiple renormalons simultaneously. Using a dual transform which suppresses infrared renormalons, we derive a one-parameter integral representation of a general observable. We investigate systematically how renormalons emerge and get canceled in the entire operator product expansion (OPE) of an observable, by applying the expansion-by-regions (EBR) method to this one-parameter integral expression. In particular we investigate in detail OPEs in a solvable model, the 2-dimensional O(N) nonlinear σ model, by the dual space approach. A nontrivial mechanism of renormalon cancellation in this model can be understood from an integration identity on which the EBR method is founded. We demonstrate that the dual space approach can be useful by a simulation study imitating the QCD case. Application of this method to QCD calculations is also discussed.

Gauged double field theory, current algebras and heterotic sigma models

We study the O(D, D + n) generalized metric and the gauge symmetries in the gauged double field theory (DFT) in view of current algebras and sigma models. We show that the O(D, D + n) generalized metric in the gauged DFT is consistent with the heterotic sigma models at the leading order in the α′-corrections. We then study the non-Abelian gauge symmetries and current algebras of heterotic string theories. We show that the algebras exhibit the correct diffeomorphism, the B-field gauge transformations of the background fields together with the non-Abelian gauge transformations possibly with the appropriate local Lorentz transformations.

Accretion disc around black hole in Einstein-SU(N) non-linear sigma model

The accretion of matter onto celestial bodies like black holes and neutron stars is a natural phenomenon that releases up to 40% of the matter’s rest-mass energy, which is considered a source of radiation. In active galactic nuclei and X-ray binaries, huge luminosities are observed as a result of accretion. Using isothermal fluid, we examine the accretion and geodesic motion of particles in the vicinity of a spherically symmetric black hole spacetime in the Einstein-SU(N) non-linear sigma model. In the accretion process, the disk-like structure is produced by the geodesic motion of particles near the black hole. We determine the innermost stable circular orbit, energy flux, radiation temperature, and radioactive efficiency numerically. In the equatorial plane, we investigate the mobility of particles with stabilities that form circular orbits. We examine perturbations of a test particle by using restoring forces and particle oscillations in the vicinity of the black hole. We analyze the maximum accretion rate and critical flow of the fluid. Our findings demonstrate how parameter N influences the circular motion of a test particle as well as the maximum accretion rate of the black hole in the Einstein-SU(N) non-linear sigma model.

On scalar charges and black hole thermodynamics

We revisit the first law of black hole thermodynamics in 4-dimensional theories containing scalar and Abelian vector fields coupled to gravity using Wald’s formalism and a new definition of scalar charge as an integral over a 2-surface which satisfies a Gauss law in the background of stationary black-hole spacetimes. We focus on ungauged supergravity-inspired theories with symmetric sigma models whose symmetries generate electric-magnetic dualities leaving invariant their equations of motion. Our manifestly duality-invariant form of the first law is compatible with the one obtained by of Gibbons, Kallosh and Kol. We also obtain the general expression for the scalar charges of a stationary black hole in terms of the other physical parameters of the solution and the position of the horizon, generalizing the expression obtained by Pacilio for dilaton black holes.

S-duality in Toverline{T} -deformed CFT

Toverline{T} deformed conformal field theories can be reformulated as worldsheet theories of non-critical strings. We use this correspondence to compute and study the Toverline{T} deformed partition sum of a symmetric product CFT. We find that it takes the form of a partition sum of a second quantized string theory with a worldsheet given by the product of the seed CFT and a gaussian sigma model with the two-torus as target space. We show that deformed symmetric product theory admits a natural UV completion that exhibits a strong weak coupling ℤ2 duality that interchanges the momentum and winding numbers and maps the Toverline{T} -coupling λ to its inverse 1/λ. The ℤ2 duality is part of a full O(2, 2, ℤ)-duality group that includes a PSL(2, ℤ) acting on the complexified Toverline{T} coupling. The duality symmetry eliminates the appearance of complex energies at strong coupling for all seed CFTs with central charge c ≤ 6.

A supersymmetric nonlinear sigma model analogue of the ModMax theory

A decade ago, it was shown that associated with any model for U(1) duality-invariant nonlinear electrodynamics there is a unique U(1) duality-invariant supersymmetric nonlinear sigma model formulated in terms of chiral and complex linear superfields. Here we study the mathcal{N} = 1 superconformal σ-model analogue of the conformal duality-invariant electrodynamics known as the ModMax theory. We derive its dual formulation in terms of chiral superfields and show that the target space is a Kähler cone with U(1) × U(1) being the connected component of the isometry group.

Green Lean Six Sigma model for waste reduction of raw material in a nectar manufacturing company of Lima, Peru

Purpose: Food waste is a latent problem for society, one of the main causes being poor management of the operating processes within the food industry, which is the main reason the present research aimed to reduce raw material waste in a nectar factory.Design/methodology/approach: The methodology led to carrying out an experimental investigation where a Green Lean Six Sigma Model was applied, whose foundation was the use of tools such as Environmental Value Stream Mapping (E - VSM), DMAIC (Define - Measure - Analyze - Improve - Control), Poka Yoke and DOE (Design of Experiments), the data obtained were exposed to an inferential statistical analysis using tests such as Anderson - Darling and T-Student.Findings: As a final result, a waste reduction of 2.23% was obtained, which is equivalent to approximately 120 kg of useful raw material, in addition the environmental impact was reduced by 2.2%, waste costs were also reduced by approximately 5.5% and produced an increase in global productivity by 2.4%.Research limitations/implications: It is shown that the application of methodologies such as Green, Lean and Six Sigma in the food industry present benefits during and after the application of the model; such as preventive control of waste, standardization in processes; benefits that, in coordination with an organizational culture of continuous improvement, can significantly improve the current state of companies.Practical implications: The positive obtained results support the methodology proposed by the authors to reduce the waste of agricultural raw material. It is expected to be a benchmark for other similar organizations that seek to generate greater productivity in line with the search for environmentally sustainable operations.Originality/value: This is one of the first studies that aims to reduce the waste of raw materials in food processing companies, considering aspects of mitigating environmental impact.

On genus-0 invariants of Calabi-Yau hybrid models

We compute genus zero correlators of hybrid phases of Calabi-Yau gauged linear sigma models (GLSMs), i.e. of phases that are Landau-Ginzburg orbifolds fibered over some base. These correlators are generalisations of Gromov-Witten and FJRW invariants. Using previous results on the structure of the of the sphere- and hemisphere partition functions of GLSMs when evaluated in different phases, we extract the I-function and the J-function from a GLSM calculation. The J-function is the generating function of the correlators. We use the field theoretic description of hybrid models to identify the states that are inserted in these correlators. We compute the invariants for examples of one- and two-parameter hybrid models. Our results match with results from mirror symmetry and FJRW theory.

Aspects of spontaneous symmetry breaking in Rindler and anti–de Sitter spacetimes for the O(N) linear sigma model

We investigate aspects of spontaneous breakdown of symmetry for $O(N)$ symmetric linear sigma model in the background of Rindler and Anti-de Sitter spacetimes respectively. In the large $N$ limit, by computing the one-loop effective action, we report that in three dimensional Rindler space, there is a phase transition from the disordered phase to an ordered phase past a certain critical Rindler acceleration parameter `$a$'. Connections with finite temperature field theory results are established, thereby further reinforcing the idea that Rindler space can indeed be a proxy for Minkowski spacetime with finite temperature. We extend our calculations to Anti-de Sitter space in various dimensions and observe that symmetry is broken in three dimensions, but not in four dimensions. We discuss the implications of our results.

Hilbert series and higher-order Lagrangians for the O(N) model

We compare the Hilbert series approach with explicit constructions of higher-order Lagrangians for the O(N) nonlinear sigma model. We use the Hilbert series to find the number and type of operators up to mass dimension 16, for spacetime dimension D up to 12 and N up to 12, and further classify the operators into spacetime parity and parity of the internal symmetry group O(N). The explicit construction of operators is done up to mass dimension 12 for both parities even and dimension 10 for the other three cases. The results of the two methods are in full agreement. This provides evidence for the Hilbert series conjecture regarding co-closed but not co-exact k-forms, which takes into account the integration-by-parts relations.

Instances of higher geometry in field theory

Generalisations of geometry have emerged in various forms in the study of field theory and quantization. This mini-review focuses on the role of higher geometry in three selected physical applications. After motivating and describing some basic aspects of algebroid structures on bundles and (differential graded) Q-manifolds, we briefly discuss their relation to $$(\alpha )$$ the Batalin–Vilkovisky quantization of topological sigma models, $$(\beta )$$ higher gauge theories and generalized global symmetries and $$(\gamma )$$ tensor gauge theories, where the universality of their form and properties in terms of graded geometry is highlighted.

Classical integrability of root- TT¯ flows

The root-$T\overline{T}$ flow was recently introduced as a universal and classically marginal deformation of any two-dimensional translation-invariant field theory. The flow commutes with the (irrelevant) $T\overline{T}$ flow, and it can be integrated explicitly for a large class of actions, leading to nonanalytic Lagrangians reminiscent of the four-dimensional modified-Maxwell theory (ModMax). It is not a priori obvious whether the root-$T\overline{T}$ flow preserves integrability, as is the case for the $T\overline{T}$ flow. In this paper we demonstrate that this is the case for a large class of classical models by explicitly constructing a deformed Lax connection. We discuss the principal chiral model and the nonlinear sigma models on symmetric and semisymmetric spaces, without or with the Wess-Zumino term. We also construct Lax connections for the two-parameter families of theories deformed by both root-$T\overline{T}$ and $T\overline{T}$ for all of these models.

Families of Q-balls in a deformed [formula omitted] linear sigma model

In this paper the existence of analytical solutions describing Q-balls in a family of deformed O(4) sigma models in (1+1) dimensions has been investigated. These models involve two complex scalar fields whose coupling breaks the O(4) symmetry group to U(1)×U(1). It has been shown that there are two types of single Q-balls rotating around each of the components of the internal space and a one-parameter family of composite Q-balls. These composite solutions consist of two single Q-balls (separated by a distance determined by the family parameter) spinning around each complex field with the same internal rotation frequency.

Integrable sigma models on Riemann surfaces

We consider quantum aspects of a class of generalized Gross-Neveu models, which in special cases reduce to sigma models. We show that, in the case of gauged models, an admissible gauge is $A_\mu=0$, which is a direct analogue of the conformal gauge in string models. Chiral anomalies are a gauge counterpart of the Weyl anomaly, and are required to vanish. Topological effects on the worldsheet lead to an integration over moduli spaces of connections on a Riemann surface. This is an initial step in studying the effects of worldsheet geometry and topology in integrable sigma models.

QCD equation of state at finite isospin density from the linear sigma model with quarks: The cold case

We use the two-flavor Linear Sigma Model with quarks to study the phase structure of isospin asymmetric matter at zero temperature. The meson degrees of freedom provide the mean field chiral and isospin condensates on top of which we compute the effective potential accounting for constituent quark fluctuations at one-loop order. Using the renormalizability of the model, we absorb the ultraviolet divergences into suitable counterterms that are added respecting the original structure of the theory. These counterterms are determined from the stability conditions which require the effective potential to have minima in the condensates directions at the classical values, as well as the transition from the noncondensed to the condensed phase to be smooth as a function of the isospin chemical potential. We use the model to study the evolution of the condensates as well as the pressure, energy and isospin densities and the sound velocity as functions of the isospin chemical potential. The approach does a good average description up to isospin chemical potentials values not too large as compared to the vacuum pion mass.

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.

Establishment and digital simulation of upper airway in patients with adenoid hypertrophy

Objective: To analyze the flow field characteristics of the upper airway in patients with different adenoid hypertrophy using computational fluid dynamics (CFD). Methods: From November 2020 to November 2021, the cone-beam CT (CBCT) data of 4 patients [2 males and 2 females,age range 5-7 years, mean (6.0±1.2) years] with adenoid hypertrophy who were hospitalized in the Department of Orthodontics and the Department of Otolaryngology at Hebei Eye Hospital were selected. The degree of adenoid hypertrophy in the 4 patients was divided into normal S1 (A/N<0.6), mild hypertrophy S2 (0.6≤A/N<0.7), moderate hypertrophy S3 (0.7≤A/N<0.9) and severe hypertrophy S4 (A/N≥0.9) according to the ratio of adenoid thickness to the width of nasopharyngeal cavity (A/N). The CFD model of the upper airway was established using ANSYS 2019 R1 software, and the internal flow field of the CFD model was numerically simulated. Eight sections were selected as observation and measurement planes for flow field information. Relevant flow field information includes airflow distribution, velocity variation, and pressure variation. Results: In the S1 model, the maximum pressure difference occurred in the 4th and 5th observation planes (ΔP=27.98). The lowest pressures and the maximum flow rates of S2 and S3 were located in the 6th observation plane. The airflow in S1 and S2 models completely passed through the nasal cavity. In the S3 model, the mouth-to-nasal airflow ratio was close to 2∶1. In S4 model, the airflow completely passed through the mouth; in the S1 and S2 models, hard palates were subjected to a downward positive pressure with a pressure difference of 38.34 and 23.31 Pa, respectively. The hard palates in S3 and S4 models were subjected to a downward negative pressure with a pressure difference of -2.95 and -21.81 Pa, respectively. Conclusions: The CFD model can objectively and quantitatively describe the upper airway airflow field information in patients with adenoid hypertrophy. With the increasing degree of adenoid hypertrophy, the nasal ventilation volume gradually decreased, whereas the oral space ventilation volume gradually increased, and the pressure difference between the upper and lower surfaces of the palate gradually decreased until the pressure became negative.

Bi-η and bi-λ deformations of ℤ4 permutation supercosets

Integrable string sigma models on AdS3 backgrounds with 16 supersymmetries have the distinguishing feature that their superisometry group is a direct product. As a result the deformation theory of these models is particularly rich since the two supergroups in the product can be deformed independently. We construct bi-η and bi-λ deformations of two classes of ℤ4 permutation supercoset sigma models, which describe sectors of the Green-Schwarz and pure-spinor string worldsheet theories on type II AdS3 backgrounds with pure R-R flux. We discuss an important limit of these models when one supergroup is undeformed. The associated deformed supergravity background should preserve 8 supersymmetries and is expected to have better properties than the full bi-deformation. As a step towards investigating the quantum properties of these models, we study the two-loop RG flow of the bosonic truncation of the bi-λ deformation.

Effective observables for electromagnetic duality from novel amplitude decomposition

We introduce a decomposition of $D$-dimensional vector amplitudes in terms of building blocks that preserve all partial amplitude relations of the parent gauge theory. Using this decomposition, we derive a new set of amplitude relations between nonlinear sigma model pions and the pure-scalar sector of Yang-Mills scalar theory. These new relations indicate an equivalence between Born-Infeld duality invariance and that of Einstein-Maxwell theory, considering their known double-copy construction from the two scalar theories with Yang-Mills. This observation motivates a general framework for constructing duality-invariant effective field theory observables at any multiplicity using the building blocks in our amplitude decomposition. Finally, we conjecture a subtle relationship between these duality-invariant building blocks and the bosonic sector of $\mathcal{N}=4$ super Yang-Mills.