scholarly journals Functional renormalization group study of the two-flavor linear sigma model in the presence of the axial anomaly

2013 ◽  
Vol 88 (5) ◽  
Author(s):  
Mara Grahl ◽  
Dirk H. Rischke
Keyword(s):  
Renormalization Group ◽  
Sigma Model ◽  
Linear Sigma Model ◽  
Functional Renormalization Group ◽  
Axial Anomaly

scholarly journals Perturbative RG Analysis of the Condensate Dependence of the Axial Anomaly in the Three-Flavor Linear Sigma Model

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 488
Author(s):  
Gergely Fejős
Keyword(s):  
Perturbation Theory ◽  
Low Temperatures ◽  
Sigma Model ◽  
Chiral Condensate ◽  
Linear Sigma Model ◽  
Zero Temperature ◽  
Renormalization Group Flow ◽  
Axial Anomaly ◽  
Field Dependent ◽  
Group Flow

Coupling of ‘t Hooft’s determinant term is investigated in the framework of the three-flavor linear sigma model as a function of the chiral condensate. Using perturbation theory around the minimum point of the effective action, we calculate the renormalization group flow of the first field-dependent correction to the coupling of the conventional UA(1) breaking determinant term. It is found that, at low temperatures, mesonic fluctuations make the anomaly increase when the chiral condensate decreases. As an application, we analyze the effect at the zero temperature nuclear liquid–gas transition.

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.

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