scholarly journals TODA FIELD THEORIES ASSOCIATED WITH HYPERBOLIC KAC-MOODY ALGEBRA — PAINLEVÉ PROPERTIES AND W ALGEBRAS

1996 ◽  
Vol 11 (31) ◽  
pp. 5479-5493 ◽  
Author(s):  
REINHOLD W. GEBERT ◽  
SHUN’YA MIZOGUCHI ◽  
TAKEO INAMI
Keyword(s):  
Lie Algebras ◽  
Energy Momentum Tensor ◽  
Direct Calculation ◽  
Momentum Tensor ◽  
Field Theories ◽  
Painlevé Analysis ◽  
Painlevé Test ◽  
Moody Algebra ◽  
Simple Lie Algebras ◽  
Conserved Currents

We show that the Painlevé test is useful not only for probing (non)integrability but also for finding the values of spins of conserved currents (W currents) in Toda field theories (TFT’s). In the case of TFT’s based on simple Lie algebras the locations of resonances are shown to give precisely the spins of conserved W currents. We apply this test to TFT’s based strictly on hyperbolic Kac-Moody algebras and show that there exist no resonance other than that at n = 2, which corresponds to the energy-momentum tensor, indicating their nonintegrability. We also check by direct calculation that there are no spin-3 or -4 conserved currents for all the hyperbolic TFT’s in agreement with the result of our Painlevé analysis.

scholarly journals Lorentzian Toda field theories

2021 ◽  
pp. 2150017
Author(s):  
Andreas Fring ◽  
Samuel Whittington
Keyword(s):  
Lie Algebras ◽  
Mass Spectra ◽  
Energy Momentum Tensor ◽  
Root Systems ◽  
Momentum Tensor ◽  
Field Theories ◽  
Simple Lie Algebras ◽  
Different Types ◽  
Algebraic Framework ◽  
Complex Valued

We propose several different types of construction principles for new classes of Toda field theories based on root systems defined on Lorentzian lattices. In analogy to conformal and affine Toda theories based on root systems of semi-simple Lie algebras, also their Lorentzian extensions come about in conformal and massive variants. We carry out the Painlevé integrability test for the proposed theories, finding in general only one integer valued resonance corresponding to the energy-momentum tensor. Thus most of the Lorentzian Toda field theories are not integrable, as the remaining resonances, that grade the spins of the W-algebras in the semi-simple cases, are either non-integer or complex valued. We analyze in detail the classical mass spectra of several massive variants. Lorentzian Toda field theories may be viewed as perturbed versions of integrable theories equipped with an algebraic framework.

scholarly journals On Sugawara construction on celestial sphere

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Wei Fan ◽  
Angelos Fotopoulos ◽  
Stephan Stieberger ◽  
Tomasz R. Taylor
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Conformal Transformations ◽  
Moody Algebra ◽  
Gauge Bosons ◽  
Yang Mills ◽  
Conformal Field ◽  
Celestial Sphere ◽  
Double Copy ◽  
Conserved Currents

Abstract Conformally soft gluons are conserved currents of the Celestial Conformal Field Theory (CCFT) and generate a Kac-Moody algebra. We study celestial amplitudes of Yang-Mills theory, which are Mellin transforms of gluon amplitudes and take the double soft limit of a pair of gluons. In this manner we construct the Sugawara energy-momentum tensor of the CCFT. We verify that conformally soft gauge bosons are Virasoro primaries of the CCFT under the Sugawara energy-momentum tensor. The Sugawara tensor though does not generate the correct conformal transformations for hard states. In Einstein-Yang- Mills theory, we consider an alternative construction of the energy-momentum tensor, similar to the double copy construction which relates gauge theory amplitudes with gravity ones. This energy momentum tensor has the correct properties to generate conformal transformations for both soft and hard states. We extend this construction to supertranslations.

scholarly journals Crystal plasticity: The Hamilton-Eshelby stress in terms of the metric in the intermediate configuration

2012 ◽  
Vol 39 (1) ◽  
pp. 55-69 ◽  
Author(s):  
Paolo Mariano
Keyword(s):  
Free Energy ◽  
Energy Momentum Tensor ◽  
Large Strain ◽  
Momentum Tensor ◽  
Classical Field ◽  
Field Theories ◽  
Relative Power ◽  
Eshelby Stress ◽  
Classical Field Theories ◽  
Intermediate Configuration

The Hamilton-Eshelby stress is a basic ingredient in the description of the evolution of point, lines and bulk defects in solids. The link between the Hamilton-Eshelby stress and the derivative of the free energy with respect to the material metric in the plasticized intermediate configuration, in large strain regime, is shown here. The result is a modified version of Rosenfeld-Belinfante theorem in classical field theories. The origin of the appearance of the Hamilton-Eshelby stress (the non-inertial part of the energy-momentum tensor) in dissipative setting is also discussed by means of the concept of relative power.

scholarly journals CANONICAL APPROACH TO 2D SUPERSYMMETRIC WZNW MODEL COUPLED TO SUPERGRAVITY

2002 ◽  
Vol 17 (29) ◽  
pp. 1923-1936 ◽  
Author(s):  
OLIVERA MIŠKOVIĆ ◽  
BRANISLAV SAZDOVIĆ
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Moody Algebra ◽  
Gauge Transformations ◽  
Local Gauge ◽  
Gauge Symmetries ◽  
Wznw Model ◽  
Canonical Approach ◽  
Explicit Expressions

Starting from the known representation of the Kac–Moody algebra in terms of the coordinates and momenta, we extend it to the representation of the super Kac–Moody and super Virasoro algebras. Then we use general canonical method to construct an action invariant under local gauge symmetries, where components of the super energy–momentum tensor L± and G± play the role of the diffeomorphisms and supersymmetry generators respectively. We obtain covariant extension of WZNW theory with respect to local supersymmetry as well as explicit expressions for gauge transformations.

SCALE AND CONFORMAL INVARIANCE AND VARIATION OF THE METRIC

2006 ◽  
Vol 21 (17) ◽  
pp. 3641-3647 ◽  
Author(s):  
J. SADEGHI ◽  
A. TOFIGHI ◽  
A. BANIJAMALI
Keyword(s):  
Conformal Invariance ◽  
Scale Invariance ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Conserved Currents

We consider the relation between scale invariance and conformal invariance. In our analysis the variation of the metric is taken into account. By imposing some conditions on the trace of the energy–momentum tensor and on the variation of the action, we find that the scale dimensions of the fields are not affected. We also obtain the conserved currents. We find that the conditions for conformal invariance are stronger than for scale invariance.

The energy-momentum tensor in scalar and gauge field theories

1974 ◽  
Vol 87 (2) ◽  
pp. 354-374 ◽  
Author(s):  
Daniel Z Freedman ◽  
Erick J Weinberg
Keyword(s):  
Gauge Field ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Gauge Field Theories ◽  
Field Theories

MATHEMATICA™ PACKAGES FOR COMPUTING PRINCIPAL DECOMPOSITIONS OF SIMPLE LIE ALGEBRAS AND APPLICATIONS IN EXTENDED CONFORMAL FIELD THEORIES

2003 ◽  
Vol 14 (01) ◽  
pp. 1-27 ◽  
Author(s):  
DANIELA GĂRĂJEU ◽  
MIHAIL GĂRĂJEU
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Three Dimensional ◽  
Adjoint Representation ◽  
Cartan Matrix ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Killing Form ◽  
Simple Lie Algebras ◽  
Conformal Field

In this article, we propose two Mathematica™ packages for doing calculations in the domain of classical simple Lie algebras. The main goal of the first package, [Formula: see text], is to determine the principal three-dimensional subalgebra of a simple Lie algebra. The package provides several functions which give some elements related to simple Lie algebras (generators in fundamental and adjoint representation, roots, Killing form, Cartan matrix, etc.). The second package, [Formula: see text], concerns the principal decomposition of a Lie algebra with respect to the principal three-dimensional embedding. These packages have important applications in extended two-dimensional conformal field theories. As an example, we present an application in the context of the theory of W-gravity.

Field theories with high derivatives

1948 ◽  
Vol 44 (1) ◽  
pp. 76-86 ◽  
Author(s):  
T. S. Chang
Keyword(s):  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Hamiltonian Formulation ◽  
Functional Derivative ◽  
Momentum Tensor ◽  
Field Theories ◽  
Field Equations ◽  
Gauge Invariant ◽  
Image Position ◽  
Derivatives Of

The relativistic field theories of elementary particles are extended to cases where the field equations are derived from Lagrangians containing all derivatives of the field quantities. Expressions for the current, the energy-momentum tensor, the angular-momentum tensor, and the symmetrized energy-momentum tensor are given. When the field interacts with an electromagnetic field, we introduce a subtraction procedure, by which all the above expressions are made gauge-invariant. The Hamiltonian formulation of the equations of motion in a gauge-invariant form is also given.After considering the Lagrangian L as a scalar in a general relativity transformation and thus a function of gμν and their derivatives, the functional derivative ofwith respect to gμν (x) at a point where the space time is flat is worked out. It is shown that this differs from the symmetrized energy-momentum tensor given in the above sections by a term which vanishes when certain operators Sij are antisymmetrical or when the Lagrangian contains the first derivatives of the field quantities only and whose divergence to either μ or ν vanishes.

On the energy-momentum tensor in gauge field theories

1974 ◽  
Vol 87 (1) ◽  
pp. 95-125 ◽  
Author(s):  
Daniel Z Freedman ◽  
Ivan J Muzinich ◽  
Erick J Weinberg
Keyword(s):  
Gauge Field ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Gauge Field Theories ◽  
Field Theories
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