scholarly journals FURTHER COMMENTS ON THE SYMMETRIC SUBTRACTION OF THE NONLINEAR SIGMA MODEL

2008 ◽  
Vol 23 (02) ◽  
pp. 211-232 ◽  
Author(s):  
DANIELE BETTINELLI ◽  
RUGGERO FERRARI ◽  
ANDREA QUADRI
Keyword(s):  
Sigma Model ◽  
Dimensional Regularization ◽  
Formal Proof ◽  
Tree Level ◽  
Nonlinear Sigma Model ◽  
Flat Connection ◽  
Subtraction Procedure ◽  
Feynman Rules ◽  
Local Functional ◽  
Two Parameters

Recently a perturbative theory has been constructed, starting from the Feynman rules of the nonlinear sigma model at the tree level in the presence of an external vector source coupled to the flat connection and of a scalar source coupled to the nonlinear sigma model constraint (flat connection formalism). The construction is based on a local functional equation, which overcomes the problems due to the presence (already at one loop) of nonchiral symmetric divergences. The subtraction procedure of the divergences in the loop expansion is performed by means of minimal subtraction of properly normalized amplitudes in dimensional regularization. In this paper we complete the study of this subtraction procedure by giving the formal proof that it is symmetric to all orders in the loopwise expansion. We provide further arguments on the issue that, within our subtraction strategy, only two parameters can be consistently used as physical constants.

scholarly journals THE SU(2) ⊗ U(1) ELECTROWEAK MODEL BASED ON THE NONLINEARLY REALIZED GAUGE GROUP

2009 ◽  
Vol 24 (14) ◽  
pp. 2639-2654 ◽  
Author(s):  
D. BETTINELLI ◽  
R. FERRARI ◽  
A. QUADRI
Keyword(s):  
Gauge Group ◽  
Dimensional Regularization ◽  
Higgs Field ◽  
Landau Gauge ◽  
Tree Level ◽  
Subtraction Procedure ◽  
Local Functional ◽  
Weinberg Angle ◽  
Electroweak Model ◽  
Intermediate Vector

The electroweak model is formulated on the nonlinearly realized gauge group SU (2) ⊗ U (1). This implies that in perturbation theory no Higgs field is present. This paper provides the effective action at the tree level, the Slavnov–Taylor identity (necessary for the proof of physical unitarity), the local functional equation (used for the control of the amplitudes involving the Goldstone bosons) and the subtraction procedure (nonstandard, since the theory is not power-counting renormalizable). Particular attention is devoted to the number of independent parameters relevant for the vector mesons; in fact, there is the possibility of introducing two mass parameters. With this choice the relation between the ratio of the intermediate vector meson masses and the Weinberg angle depends on an extra free parameter. We briefly outline a method for dealing with γ5 in dimensional regularization. The model is formulated in the Landau gauge for sake of simplicity and conciseness. The QED Ward identity has a simple and intriguing form.

RENORMALIZATION GROUP FLOW AND OPEN STRING DYNAMICS

1988 ◽  
Vol 03 (18) ◽  
pp. 1797-1805 ◽  
Author(s):  
NAOHITO NAKAZAWA ◽  
KENJI SAKAI ◽  
JIRO SODA
Keyword(s):  
Renormalization Group ◽  
Sigma Model ◽  
Open String ◽  
Tree Level ◽  
Nonlinear Sigma Model ◽  
Renormalization Group Flow ◽  
Point Solution ◽  
Β Function ◽  
Group Flow ◽  
Model Approach

The renormalization group flow in the nonlinear sigma model approach is explicitly solved to the fourth order in the case of an open string propagating in the tachyon background. Using a regularization different from the original one used by Klebanov and Susskind (K-S), we show that its fixed point solution produces the tree-level 5-point tachyon amplitude. Furthermore we prove K-S’s conjecture, i.e., the equivalence between the vanishing β-function defined by our regularization and the equation of motion arising from the effective action, up to all orders.

SOLITON OPERATORS OF FRACTIONAL SPIN IN 2+1 DIMENSIONS

1991 ◽  
Vol 06 (08) ◽  
pp. 1369-1383 ◽  
Author(s):  
DIMITRA KARABALI
Keyword(s):  
Configuration Space ◽  
Sigma Model ◽  
Canonical Quantization ◽  
Nonlinear Sigma Model ◽  
Flat Connection ◽  
Fractional Spin ◽  
Spin And Statistics

Soliton operators of fractional spin and statistics are constructed using canonical quantization of the O(3) nonlinear sigma model with a topological Hopf action in 2+1 dimensions. The role of the Hopf term as the nontrivial holonomy of a flat connection in the configuration space is emphasized.

scholarly journals Erratum to: Higher-order tree-level amplitudes in the nonlinear sigma model

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Johan Bijnens ◽  
Karol Kampf ◽  
Mattias Sjö
Keyword(s):  
Sigma Model ◽  
Higher Order ◽  
Tree Level ◽  
Nonlinear Sigma Model ◽  
Supplementary Material

In the original paper the supplementary material was incorrect and incomplete. The correct supplementary material is attached to this erratum.

scholarly journals Higher-order tree-level amplitudes in the nonlinear sigma model

2019 ◽  
Vol 2019 (11) ◽  
Author(s):  
Johan Bijnens ◽  
Karol Kampf ◽  
Mattias Sjö
Keyword(s):  
Sigma Model ◽  
Higher Order ◽  
Tree Level ◽  
Nonlinear Sigma Model

scholarly journals Tree-level amplitudes in the nonlinear sigma model

2013 ◽  
Vol 2013 (5) ◽  
Author(s):  
Karol Kampf ◽  
Jirí Novotný ◽  
Jaroslav Trnka
Keyword(s):  
Sigma Model ◽  
Tree Level ◽  
Nonlinear Sigma Model

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.

scholarly journals Vector–Tensor Duality

1997 ◽  
Vol 12 (35) ◽  
pp. 2699-2705 ◽  
Author(s):  
Amitabha Lahiri
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Flat Connection ◽  
Mass Generation ◽  
Goldstone Bosons ◽  
Abelian Case ◽  
Vector Bosons ◽  
Topological Mass

A dynamical non-Abelian two-form potential gives masses to vector bosons via a topological coupling.1 Unlike in the Abelian case, the two-form cannot be dualized to Goldstone bosons. Duality is restored by coupling a flat connection to the theory in a particular way, and the new action is then dualized to a nonlinear sigma model. The presence of the flat connection is crucial, which saves the original mechanism of Higgs-free topological mass generation from being dualized to a sigma model.

Sign in / Sign up

Export Citation Format

Share Document