scholarly journals Weak Power-Counting Theorem for the Renormalization of the Nonlinear Sigma Model in Four Dimensions

2006 ◽  
Vol 45 (12) ◽  
pp. 2497-2515 ◽  
Author(s):  
Ruggero Ferrari ◽  
Andrea Quadri
Keyword(s):  
Sigma Model ◽  
Power Counting ◽  
Nonlinear Sigma Model ◽  
Four Dimensions

scholarly journals Massive gravity from double copy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Arshia Momeni ◽  
Justinas Rumbutis ◽  
Andrew J. Tolley
Keyword(s):  
Sigma Model ◽  
Massive Gravity ◽  
Effective Field ◽  
Effective Theory ◽  
Nonlinear Sigma Model ◽  
Limit Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Massive Spin ◽  
Double Copy

Abstract We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

scholarly journals NONCOMMUTATIVE U(1) GAUGE THEORY AS A NONLINEAR SIGMA MODEL

2004 ◽  
Vol 19 (29) ◽  
pp. 2205-2213 ◽  
Author(s):  
BADIS YDRI
Keyword(s):  
Gauge Theory ◽  
Sigma Model ◽  
Beta Function ◽  
Scaling Limit ◽  
Two Dimensions ◽  
Nonlinear Sigma Model ◽  
Matrix Size ◽  
Gauge Groups ◽  
Four Dimensions ◽  
The Matrix

Noncommutative U (1) gauge theory in four dimensions is shown to be equivalent in some scaling limit to an ordinary nonlinear sigma model in two dimensions. The model in this regime is solvable and the corresponding exact beta function is found. We also show that classical U (n) gauge theory on [Formula: see text] can be approximated by a sequence of ordinary (d-2)-dimensional Georgi–Glashow models with gauge groups U (n(L+1)), where L+1 is the matrix size of the regularized noncommutative plane [Formula: see text].

scholarly journals The nonlinear sigma model and spin ladders

1996 ◽  
Vol 29 (12) ◽  
pp. 3299-3310 ◽  
Author(s):  
Germán Sierra
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model

scholarly journals An emergent universe supported by a nonlinear sigma model

2009 ◽  
Vol 26 (7) ◽  
pp. 075017 ◽  
Author(s):  
A Beesham ◽  
S V Chervon ◽  
S D Maharaj
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Emergent Universe

scholarly journals Isolated skyrmions in the CP2 nonlinear sigma model with a Dzyaloshinskii-Moriya type interaction

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Yutaka Akagi ◽  
Yuki Amari ◽  
Nobuyuki Sawado ◽  
Yakov Shnir
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Type Interaction

scholarly journals GAUSS DECOMPOSITION, WAKIMOTO REALIZATION AND GAUGED WZNW MODELS

1994 ◽  
Vol 09 (11) ◽  
pp. 1009-1023
Author(s):  
H. ARFAEI ◽  
N. MOHAMMEDI
Keyword(s):  
Field Strength ◽  
Sigma Model ◽  
Target Space ◽  
Gauge Fields ◽  
Nonlinear Sigma Model ◽  
Model Interpretation ◽  
Gauss Decomposition ◽  
Wznw Model ◽  
Wakimoto Realization

The implications of gauging the Wess-Zumino-Novikov-Witten (WZNW) model using the Gauss decomposition of the group elements are explored. We show that, contrary to the standard gauging of WZNW models, this gauging is carried out by minimally coupling the gauge fields. We find that this gauging, in the case of gauging and Abelian vector subgroup, differs from the standard one by terms proportional to the field strength of the gauge fields. We prove that gauging an Abelian vector subgroup does not have a nonlinear sigma model interpretation. This is because the target-space metric resulting from the integration over the gauge fields is degenerate. We demonstrate, however, that this kind of gauging has a natural interpretation in terms of Wakimoto variables.

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