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

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.

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 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 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 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 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
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