scholarly journals Linear sigma model for multiflavor gauge theories

2017 ◽  
Vol 96 (11) ◽  
Author(s):  
Y. Meurice
Keyword(s):  
Sigma Model ◽  
Gauge Theories ◽  
Linear Sigma Model

scholarly journals Undoing decomposition

2019 ◽  
Vol 34 (35) ◽  
pp. 1950233 ◽  
Author(s):  
Eric Sharpe
Keyword(s):  
Sigma Model ◽  
Gauge Theories ◽  
Disjoint Union ◽  
Path Integrals ◽  
Two Dimensions ◽  
Linear Sigma Model ◽  
Two Dimensional ◽  
Yang Mills ◽  
Witten Theory ◽  
Supersymmetric Gauge

In this paper we discuss gauging one-form symmetries in two-dimensional theories. The existence of a global one-form symmetry in two dimensions typically signals a violation of cluster decomposition — an issue resolved by the observation that such theories decompose into disjoint unions, a result that has been applied to, for example, Gromov–Witten theory and gauged linear sigma model phases. In this paper we describe how gauging one-form symmetries in two-dimensional theories can be used to select particular elements of that disjoint union, effectively undoing decomposition. We examine such gaugings explicitly in examples involving orbifolds, nonsupersymmetric pure Yang–Mills theories, and supersymmetric gauge theories in two dimensions. Along the way, we learn explicit concrete details of the topological configurations that path integrals sum over when gauging a one-form symmetry, and we also uncover “hidden” one-form symmetries.

scholarly journals Can a Linear Sigma Model Describe Walking Gauge Theories at Low Energies?

2018 ◽  
Vol 175 ◽  
pp. 08024 ◽  
Author(s):  
Andrew Gasbarro
Keyword(s):  
Sigma Model ◽  
Gauge Theories ◽  
Pion Mass ◽  
Effective Field ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Lattice Data ◽  
Conformal Window ◽  
Quark Masses ◽  
Low Energies

In recent years, many investigations of confining Yang Mills gauge theories near the edge of the conformal window have been carried out using lattice techniques. These studies have revealed that the spectrum of hadrons in nearly conformal ("walking") gauge theories differs significantly from the QCD spectrum. In particular, a light singlet scalar appears in the spectrum which is nearly degenerate with the PNGBs at the lightest currently accessible quark masses. This state is a viable candidate for a composite Higgs boson. Presently, an acceptable effective field theory (EFT) description of the light states in walking theories has not been established. Such an EFT would be useful for performing chiral extrapolations of lattice data and for serving as a bridge between lattice calculations and phenomenology. It has been shown that the chiral Lagrangian fails to describe the IR dynamics of a theory near the edge of the conformal window. Here we assess a linear sigma model as an alternate EFT description by performing explicit chiral fits to lattice data. In a combined fit to the Goldstone (pion) mass and decay constant, a tree level linear sigma model has a Χ2/d.o.f. = 0.5 compared to Χ2/d.o.f. = 29.6 from fitting nextto-leading order chiral perturbation theory. When the 0++ (σ) mass is included in the fit, Χ2/d.o.f. = 4.9. We remark on future directions for providing better fits to the σ mass.

scholarly journals Long way to Ricci flatness

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Jin Chen ◽  
Chao-Hsiang Sheu ◽  
Mikhail Shifman ◽  
Gianni Tallarita ◽  
Alexei Yung
Keyword(s):  
Sigma Model ◽  
Ultra Violet ◽  
The Other ◽  
Target Space ◽  
Linear Sigma Model ◽  
Close Relative ◽  
Two Dimensional ◽  
World Sheet ◽  
Ricci Flat ◽  
The World

Abstract We study two-dimensional weighted $$ \mathcal{N} $$ N = (2) supersymmetric ℂℙ models with the goal of exploring their infrared (IR) limit. 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) are simplified versions of world-sheet theories on non-Abelian strings in four-dimensional $$ \mathcal{N} $$ N = 2 QCD. In the gauged linear sigma model (GLSM) formulation, 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) has N charges +1 and $$ \tilde{N} $$ N ˜ charges −1 fields. As well-known, at $$ \tilde{N} $$ N ˜ = N this GLSM is conformal. Its target space is believed to be a non-compact Calabi-Yau manifold. We mostly focus on the N = 2 case, then the Calabi-Yau space is a conifold. On the other hand, in the non-linear sigma model (NLSM) formulation the model has ultra-violet logarithms and does not look conformal. Moreover, its metric is not Ricci-flat. We address this puzzle by studying the renormalization group (RG) flow of the model. We show that the metric of NLSM becomes Ricci-flat in the IR. Moreover, it tends to the known metric of the resolved conifold. We also study a close relative of the 𝕎ℂℙ model — the so called zn model — which in actuality represents the world sheet theory on a non-Abelian semilocal string and show that this zn model has similar RG properties.

scholarly journals Magnetic field dependence of the neutral pion mass in the linear sigma model with quarks: The strong field case

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Alejandro Ayala ◽  
José Luis Hernández ◽  
L. A. Hernández ◽  
Ricardo L. S. Farias ◽  
R. Zamora
Keyword(s):  
Magnetic Field ◽  
Field Dependence ◽  
Magnetic Field Dependence ◽  
Sigma Model ◽  
Neutral Pion ◽  
Strong Field ◽  
Pion Mass ◽  
Linear Sigma Model ◽  
Field Case

scholarly journals Gauged linear sigma model and pion-pion scattering

2009 ◽  
Vol 80 (11) ◽  
Author(s):  
Amir H. Fariborz ◽  
N. W. Park ◽  
Joseph Schechter ◽  
M. Naeem Shahid
Keyword(s):  
Sigma Model ◽  
Linear Sigma Model ◽  
Pion Scattering ◽  
Gauged Linear Sigma Model

scholarly journals Using the Linear Sigma Model with quarks to describe the QCD phase diagram and to locate the critical end point

2018 ◽  
Vol 172 ◽  
pp. 08002
Author(s):  
Alejandro Ayala ◽  
Jorge David Castaño-Yepes ◽  
José Antonio Flores ◽  
Saúl Hernández ◽  
Luis Hernández
Keyword(s):  
Phase Diagram ◽  
Critical Temperature ◽  
Sigma Model ◽  
Chemical Potential ◽  
Linear Sigma Model ◽  
Transition Line ◽  
Baryon Chemical Potential ◽  
First Order ◽  
Qcd Phase Diagram ◽  
Crossover Transition

We study the QCD phase diagram using the linear sigma model coupled to quarks. We compute the effective potential at finite temperature and quark chemical potential up to ring diagrams contribution. We show that, provided the values for the pseudo-critical temperature Tc = 155 MeV and critical baryon chemical potential μBc ≃ 1 GeV, together with the vacuum sigma and pion masses. The model couplings can be fixed and that these in turn help to locate the region where the crossover transition line becomes first order.

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