scholarly journals Embedding nonlinear sigma model into super-Yang–Mills theory

2009 ◽  
Vol 807 (3) ◽  
pp. 397-423 ◽  
Author(s):  
B. Basso ◽  
G.P. Korchemsky
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Yang Mills ◽  
Super Yang Mills Theory

NON-RENORMALIZABILITY OF THE MASSIVE N = 2 SUPER-YANG–MILLS THEORY

1991 ◽  
Vol 06 (23) ◽  
pp. 2143-2154 ◽  
Author(s):  
G. A. KHELASHVILI ◽  
V. I. OGIEVETSKY
Keyword(s):  
Perturbation Theory ◽  
Fourth Order ◽  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Harmonic Superspace ◽  
Yang Mills ◽  
Super Yang Mills Theory

The massive N = 2 supersymmetric Yang–Mills theory is investigated. Its non-renormalizability is revealed starting from the fourth order of the perturbation theory. The N = 2 harmonic superspace approach and the Stueckelberg-like formalism are used. The Stueckelberg fields form some nonlinear sigma model. Non-renormalizability of the latter produces non-renormalizability of the N = 2 supersymmetric Yang–Mills theory.

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.

A CONDENSED MATTER ANALOG OF QCD WITH QUARKS

1994 ◽  
Vol 08 (04) ◽  
pp. 417-428
Author(s):  
R. SHANKAR
Keyword(s):  
Relativistic Theory ◽  
Sigma Model ◽  
Condensed Matter ◽  
Quantum Spin ◽  
Spin Chains ◽  
Nonlinear Sigma Model ◽  
Dirac Fermions ◽  
Quantum Spin Chains ◽  
Yang Mills ◽  
Gauge Interaction

It is well known that the d = 1 + 1 nonlinear sigma model is a remarkable analog of pure Yang-Mills theory in d = 3 + 1 and that the former in turn arises in the study of Quantum Spin Chains. It is shown that, upon doping with holes, the chain is described by a fully relativistic theory of Dirac fermions coupled to the sigma model by a gauge interaction. The theory is seen to mimic QCD with quarks in many remarkable ways.

scholarly journals Solitons of Some Nonlinear Sigma-Like Models

2020 ◽  
Author(s):  
V.E. Vekslerchik ◽  
Keyword(s):  
Sigma Model ◽  
Soliton Solutions ◽  
Nonlinear Sigma Model ◽  
Two Dimensional ◽  
Differential Identities ◽  
Yang Mills ◽  
Class Of Matrices

We present a set of differential identities for some class of matrices. These identities are used to derive the N-soliton solutions for the Pohlmeyer nonlinear sigma-model, two-dimensional self-dual Yang-Mills equations and some modification of the vector Calapso equation.

scholarly journals Higher-Dimensional WZW Model on Kähler Manifold and Toroidal Lie Algebra

1997 ◽  
Vol 12 (36) ◽  
pp. 2757-2764 ◽  
Author(s):  
Takeo Inami ◽  
Tatsuya Ueno ◽  
Hiroaki Kanno
Keyword(s):  
Lie Algebra ◽  
Sigma Model ◽  
Kähler Manifold ◽  
Classical Equation ◽  
Nonlinear Sigma Model ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Kahler Manifold ◽  
Higher Dimensional ◽  
Toroidal Lie Algebra

We construct a generalization of the two-dimensional Wess–Zumino–Witten model on a 2n-dimensional Kähler manifold as a group-valued nonlinear sigma model with an anomaly term containing the Kähler form. The model is shown to have an infinite-dimensional symmetry which generates an n-toroidal Lie algebra. The classical equation of motion turns out to be the Donaldson–Uhlenbeck–Yau equation, which is a 2n-dimensional generalization of the self-dual Yang–Mills equation.

scholarly journals Symmetry restoration and the gluon mass in the Landau gauge

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Urko Reinosa ◽  
Julien Serreau ◽  
Rodrigo Carmo Terin ◽  
Matthieu Tissier
Keyword(s):  
Field Theory ◽  
Sigma Model ◽  
Landau Gauge ◽  
Two Dimensions ◽  
Nonlinear Sigma Model ◽  
Yang Mills ◽  
Local Field Theory ◽  
Gauge Fixing ◽  
Gribov Ambiguity ◽  
Gribov Copies

We investigate the generation of a gluon screening mass in Yang-Mills theory in the Landau gauge. We propose a gauge-fixing procedure where the Gribov ambiguity is overcome by summing over all Gribov copies with some weight function. This can be formulated in terms of a local field theory involving constrained, nonlinear sigma model fields. We show that a phenomenon of radiative symmetry restoration occurs in this theory, similar to what happens in the standard nonlinear sigma model in two dimensions. This results in a nonzero gluon screening mass, as seen in lattice simulations.

scholarly journals Covariant color-kinematics duality

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Clifford Cheung ◽  
James Mangan
Keyword(s):  
Sigma Model ◽  
Equations Of Motion ◽  
Explicit Construction ◽  
Tree Level ◽  
Nonlinear Sigma Model ◽  
Yang Mills ◽  
Novel Structure ◽  
Double Copy ◽  
Number Of Particles ◽  
Field Strengths

Abstract We show that color-kinematics duality is a manifest property of the equations of motion governing currents and field strengths. For the nonlinear sigma model (NLSM), this insight enables an implementation of the double copy at the level of fields, as well as an explicit construction of the kinematic algebra and associated kinematic current. As a byproduct, we also derive new formulations of the special Galileon (SG) and Born-Infeld (BI) theory.For Yang-Mills (YM) theory, this same approach reveals a novel structure — covariant color-kinematics duality — whose only difference from the conventional duality is that 1/□ is replaced with covariant 1/D2. Remarkably, this structure implies that YM theory is itself the covariant double copy of gauged biadjoint scalar (GBAS) theory and an F3 theory of field strengths encoding a corresponding kinematic algebra and current. Directly applying the double copy to equations of motion, we derive general relativity (GR) from the product of Einstein-YM and F3 theory. This exercise reveals a trivial variant of the classical double copy that recasts any solution of GR as a solution of YM theory in a curved background.Covariant color-kinematics duality also implies a new decomposition of tree-level amplitudes in YM theory into those of GBAS theory. Using this representation we derive a closed-form, analytic expression for all BCJ numerators in YM theory and the NLSM for any number of particles in any spacetime dimension. By virtue of the double copy, this constitutes an explicit formula for all tree-level scattering amplitudes in YM, GR, NLSM, SG, and BI.

TWO-DIMENSIONAL (4,4) SUPERSYMMETRY AND NON-ABELIAN DUALITY

1999 ◽  
Vol 14 (32) ◽  
pp. 5093-5104 ◽  
Author(s):  
F. ASSAOUI ◽  
N. BENHAMOU ◽  
T. LHALLABI
Keyword(s):  
Sigma Model ◽  
Two Dimensional ◽  
Gauge Action ◽  
Yang Mills ◽  
Gauge Anomaly ◽  
Super Yang Mills Theory

The (4,4) supersymmetric dual gauge action of the two-dimensional (4,4) super-Yang–Mills theory is constructed and the corresponding gauge anomaly is expressed. The Abelian and non-Abelian T duality of the two-dimensional (4,4) supersymmetric sigma model are discussed.

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