scholarly journals Operator product expansion on the lattice: a numerical test in the two-dimensional non-linear sigma-model

2000 ◽  
Vol 2000 (09) ◽  
pp. 045-045 ◽  
Author(s):  
Sergio Caracciolo ◽  
Andrea Montanari ◽  
Andrea Pelissetto
Keyword(s):  
Operator Product Expansion ◽  
Sigma Model ◽  
Numerical Test ◽  
Linear Sigma Model ◽  
Operator Product ◽  
Two Dimensional ◽  
Non Linear

REINTERPRETATION OF THE NON-LINEAR SIGMA MODEL WITH TORSION

1988 ◽  
Vol 03 (18) ◽  
pp. 1791-1796 ◽  
Author(s):  
J. GEGENBERG ◽  
P.F. KELLY ◽  
R.B. MANN ◽  
R. MCARTHUR ◽  
D. VINCENT
Keyword(s):  
Sigma Model ◽  
Linear Sigma Model ◽  
Two Dimensional ◽  
Global Features ◽  
Non Linear

It is shown that the bosonic non-linear sigma model with torsion may be reinterpreted as a non-linear sigma model formulated on an algebraically extended two-dimensional worldsheet. The torsion term arises naturally as a consequence of the extended geometry. The two models, while locally equivalent, have distinct global features.

scholarly journals Monte Carlo simulations for the two-dimensional O(3) non-linear sigma model

1981 ◽  
Vol 100 (6) ◽  
pp. 485-488 ◽  
Author(s):  
G. Martinelli ◽  
G. Parisi ◽  
R. Petronzio
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Sigma Model ◽  
Linear Sigma Model ◽  
Two Dimensional ◽  
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.

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