scholarly journals Testing the Bethe ansatz with large N renormalons

2021 ◽  
Author(s):  
Marcos Mariño ◽  
Ramon Miravitllas ◽  
Tomás Reis
Keyword(s):  
Bethe Ansatz ◽  
Sigma Model ◽  
State Energy ◽  
Beta Function ◽  
Linear Sigma Model ◽  
Leading Order ◽  
Supersymmetric Extension ◽  
Direct Derivation ◽  
Large N ◽  
Precise Prediction

AbstractThe ground-state energy of integrable asymptotically free theories can be conjecturally computed using the Bethe ansatz once the theory has been coupled to an external potential through a conserved charge. This leads to a precise prediction for the perturbative expansion of the energy. We provide a non-trivial test of this prediction in the non-linear sigma model and its supersymmetric extension, by calculating analytically the associated Feynman diagrams at next-to-leading order in the 1/N expansion, and at all loops. By investigating the large order behavior of the diagrams, we locate the position of the renormalons of the theory and we obtain an analytic expression for the large N trans-series associated to each. As a spin-off of our calculation, we provide a direct derivation of the beta function of these theories, at next-to-leading order in the 1/N expansion.

scholarly journals Chiral Perturbation Theory vs. Linear Sigma Model in a Chiral Imbalance Medium

Particles ◽  
2020 ◽  
Vol 3 (1) ◽  
pp. 15-22 ◽  
Author(s):  
Alexander Andrianov ◽  
Vladimir Andrianov ◽  
Domenec Espriu
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Sigma Model ◽  
Decay Constant ◽  
Low Energy ◽  
Linear Sigma Model ◽  
Chiral Perturbation ◽  
Large N ◽  
Energy Quantum ◽  
Energy Constants

We compare the chiral perturbation theory (ChPT) and the linear sigma model (LSM) as realizations of low energy quantum chromodynamics (QCD) for light mesons in a chirally-imbalanced medium. The relations between the low-energy constants of the chiral Lagrangian and the corresponding constants of the linear sigma model are established as well as the expressions for the decay constant of π -meson in the medium and for the mass of the a 0 . In the large N c count taken from QCD the correspondence of ChPT and LSM is remarkably good and provides a solid ground for the search of chiral imbalance manifestations in pion physics. A possible experimental detection of chiral imbalance (and therefore a phase with local parity breaking) is outlined in the charged pion decays inside the fireball.

scholarly journals Bethe ansatz for quantum-deformed strings

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Fiona K. Seibold ◽  
Alessandro Sfondrini
Keyword(s):  
Bethe Ansatz ◽  
Transfer Matrix ◽  
Sigma Model ◽  
Linear Sigma Model ◽  
Asymptotic Spectrum ◽  
Integrable Structure ◽  
Conserved Charges ◽  
Integrable Quantum ◽  
Quantum Deformations ◽  
Bethe Equations

Abstract Two distinct η-deformations of strings on AdS5×S5 can be defined; both amount to integrable quantum deformations of the string non-linear sigma model, but only one is itself a superstring background. In this paper we compare their conjectured all-loop worldsheet S matrices and derive the corresponding Bethe equations. We find that, while the S matrices are apparently different, they lead to the same Bethe equations. Moreover, in either case the eigenvalues of the transfer matrix, which encode the conserved charges of each system, also coincide. We conclude that the integrable structure underlying the two constructions is essentially the same. Finally, we write down the full Bethe-Yang equations describing the asymptotic spectrum of the superstring background.

scholarly journals Order parameter dynamics of the non-linear sigma model in the large N limit

2020 ◽  
Vol 93 (3) ◽  
Author(s):  
Sebastian Gemsheim ◽  
Ipsita Mandal ◽  
Krishnendu Sengupta ◽  
Zhiqiang Wang
Keyword(s):  
Order Parameter ◽  
Sigma Model ◽  
Linear Sigma Model ◽  
Large N ◽  
Non Linear

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
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