scholarly journals STAIRCASE MODELS FROM AFFINE TODA FIELD THEORY

1993 ◽  
Vol 08 (05) ◽  
pp. 873-893 ◽  
Author(s):  
PATRICK DOREY ◽  
FRANCESCO RAVANINI
Keyword(s):  
Field Theory ◽  
Elastic Scattering ◽  
Lie Algebras ◽  
Bethe Ansatz ◽  
Minimal Model ◽  
Coupling Constants ◽  
Field Theories ◽  
Thermodynamic Bethe Ansatz ◽  
Group Flow ◽  
Toda Field Theory

We propose a class of purely elastic scattering theories generalising the staircase model of Al. B. Zamolodchikov, based on the affine Toda field theories for simply-laced Lie algebras g=A, D, E at suitable complex values of their coupling constants. Considering their Thermodynamic Bethe Ansatz (TBA) equations, we give analytic arguments in support of a conjectured renormalisation group flow visiting the neighbourhood of each Wg minimal model in turn.

CONFORMAL AFFINE TODA FIELD THEORIES

1992 ◽  
Vol 06 (11n12) ◽  
pp. 2015-2040 ◽  
Author(s):  
L. BONORA
Keyword(s):  
Field Theory ◽  
Field Theories ◽  
The Continuum ◽  
Toda Field Theory

The conformal affine sl2 Toda field theory is introduced and analyzed both in the continuum and on the lattice.

scholarly journals Thermodynamic Bethe Ansatz for Biscalar Conformal Field Theories in any Dimension

2020 ◽  
Vol 125 (9) ◽  
Author(s):  
Benjamin Basso ◽  
Gwenaël Ferrando ◽  
Vladimir Kazakov ◽  
De-liang Zhong
Keyword(s):  
Bethe Ansatz ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Thermodynamic Bethe Ansatz ◽  
Conformal Field

scholarly journals THERMODYNAMIC BETHE ANSATZ AND THREE-FOLD TRIANGULATIONS

1996 ◽  
Vol 11 (22) ◽  
pp. 4051-4064 ◽  
Author(s):  
F. GLIOZZI ◽  
R. TATEO
Keyword(s):  
Bethe Ansatz ◽  
Unknown Function ◽  
Functional Equations ◽  
Simple Solution ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Thermodynamic Bethe Ansatz ◽  
Ansatz Approach ◽  
General Explanation

In the thermodynamic Bethe ansatz approach to 2D integrable, ADE-related quantum field theories, one derives a set of algebraic functional equations (a Y system) which play a prominent role. This set of equations is mapped onto the problem of finding finite triangulations of certain 3D manifolds. This mapping allows us to find a general explanation of the periodicity of the Y system. For the AN related theories, and more generally for the various restrictions of the fractionally supersymmetric sine—Gordon models, we find an explicit, surprisingly simple solution of such functional equations in terms of a single unknown function of the rapidity. The recently found dilogarithm functional equations associated to the Y system simply express the invariance of the volume of a manifold for deformations of its triangulations.

scholarly journals Hyperbolic deformation of a gauge field theory and the hierarchy problem

2016 ◽  
Vol 31 (34) ◽  
pp. 1650177 ◽  
Author(s):  
R. Cartas-Fuentevilla ◽  
A. Escalante-Hernandez ◽  
A. Herrera-Aguilar
Keyword(s):  
Field Theory ◽  
Electromagnetic Coupling ◽  
Coupling Constants ◽  
Fine Tuning ◽  
Mass Hierarchy ◽  
Symmetry Breakdown ◽  
Hybrid Parts ◽  
Gauge Hierarchy ◽  
Mass Terms ◽  
Group Flow

The problem of the gauge hierarchy is brought up in a hypercomplex scheme for a [Formula: see text] field theory; in such a scheme, a compact gauge group is deformed through a [Formula: see text]-parameter that varies along a noncompact internal direction, transverse to the [Formula: see text] compact one, and thus an additional [Formula: see text] gauge symmetry is incorporated. This transverse direction can be understood as an extra internal dimension, which will control the spontaneous symmetry breakdown, and will allow us to establish a mass hierarchy. In this mechanism, there is no brane separation to be estabilized as in the braneworld paradigm, however, a different kind of fine-tuning is needed in order to generate the wished electroweak/Planck hierarchy. By analyzing the effective self-interactions and mass terms of the theory, an interesting duality is revealed between the real and hybrid parts of the effective potential. This duality relates the weak and strong self-interaction regimes of the theory, due to the fact that both mass terms and self-coupling constants appear as one-parameter flows in [Formula: see text]. Additionally, the [Formula: see text]-deformation will establish a flow for the electromagnetic coupling that mimics the renormalization group flow for the charge in QED.

ON THE VANISHING COUPLINGS IN $\hat{A}\hat{D}\hat{E}$ AFFINE TODA FIELD THEORIES

1992 ◽  
Vol 07 (23) ◽  
pp. 5707-5718
Author(s):  
YOSHIHIRO SAITOH ◽  
TOKUZO SHIMADA
Keyword(s):  
Field Theory ◽  
Field Theories ◽  
Charge Balance ◽  
Massless Theory ◽  
Balance Condition ◽  
Interaction Terms ◽  
Exponential Interaction ◽  
A Charge ◽  
Higher Order Corrections ◽  
Toda Field Theory

We show that certain vanishing couplings in the [Formula: see text] affine Toda field theories remain vanishing even after higher-order corrections are included. This is a requisite property for the Lagrangian formulation of the theory. We develop a new perturbative formulation and treat affine Toda field theories as a massless theory with exponential interaction terms. We show that the nonrenormalization comes from the Dynkin automorphism of the Lie algebra associated with these theories. A charge balance condition plays an important role in our scheme. The all-order nonrenormalization of vanishing couplings in [Formula: see text] affine Toda field theory is also proved in a standard massive scheme.

scholarly journals USING CONSERVATION LAWS TO SOLVE TODA FIELD THEORIES

1996 ◽  
Vol 11 (10) ◽  
pp. 1831-1853 ◽  
Author(s):  
ERLING G.B. HOHLER ◽  
KÅRE OLAUSSEN
Keyword(s):  
Field Theory ◽  
Differential Equations ◽  
Conservation Laws ◽  
Closed System ◽  
Transformation Group ◽  
Field Theories ◽  
Real Form ◽  
Local Conservation ◽  
Considerable Detail ◽  
Toda Field Theory

We investigate the question of how the knowledge of sufficiently many local conservation laws for a model can be used to solve it. We show that for models where the conservation laws can be written in one-sided forms, [Formula: see text] like the problem can always be reduced to solving a closed system of ordinary differential equations. We investigate the A1, A2 and B2 Toda field theories in considerable detail from this viewpoint. One of our findings is that there is in each case a transformation group intrinsic to the model. This group is built on a specific real form of the Lie algebra used to label the Toda field theory. It is the group of field transformations which leaves the conserved densities invariant.

scholarly journals BOUNDARY BOUND STATES IN AFFINE TODA FIELD THEORY

1995 ◽  
Vol 10 (05) ◽  
pp. 739-751 ◽  
Author(s):  
ANDREAS FRING ◽  
ROLAND KÖBERLE
Keyword(s):  
Field Theory ◽  
Bound States ◽  
Dynkin Diagram ◽  
Binding Energies ◽  
Field Theories ◽  
Complete Set ◽  
Reflecting Boundaries ◽  
Toda Field Theory

We demonstrate that the generalization of the Coleman–Thun mechanism may be applied to the situation where one considers scattering processes in 1 + 1 dimensions in the presence of reflecting boundaries. For affine Toda field theories we find that the binding energies of the bound states are always half the sum over a set of masses having the same color with respect to the bicoloration of the Dynkin diagram. For the case of E6 affine Toda field theory we compute explicitly the spectrum of all higher boundary bound states. The complete set of states constitutes a closed bootstrap.

THE AFFINE TODA S-MATRICES vs PERTURBATION THEORY

1993 ◽  
Vol 08 (01) ◽  
pp. 115-134 ◽  
Author(s):  
RYU SASAKI ◽  
FREDDY PERMANA ZEN
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Fourth Order ◽  
Calculation Method ◽  
Coupling Constants ◽  
Matrix Approach ◽  
Bootstrap Equation ◽  
S Matrix ◽  
Complete Form ◽  
Toda Field Theory

We present perturbative calculations for the Affine Toda Field Theory (ATFT) S-matrices to the second order in the coupling constants for [Formula: see text] and [Formula: see text] in general, to the fourth order for [Formula: see text] theory as well as to the sixth order for [Formula: see text] theory. Conventional Feynman–Dyson calculation method and the dispersion approach are used to calculate the complete form of the perturbation amplitudes in contrast to the pole residues in previous papers. The results agree with those S-matrices obtained in the S-matrix approach, namely those based on analyticity, unitarity, crossing and bootstrap equation.

scholarly journals PERTURBATIVE SYMMETRIES ON NONCOMMUTATIVE SPACES

2004 ◽  
Vol 19 (32) ◽  
pp. 5693-5706 ◽  
Author(s):  
CHRISTIAN BLOHMANN
Keyword(s):  
Field Theory ◽  
Lie Algebras ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Plane ◽  
Star Products ◽  
Quantum Field ◽  
Enveloping Algebras ◽  
Noncommutative Spaces ◽  
Noncommutative Quantum

Perturbative deformations of symmetry structures on noncommutative spaces are studied in view of noncommutative quantum field theories. The rigidity of enveloping algebras of semisimple Lie algebras with respect to formal deformations is reviewed in the context of star products. It is shown that rigidity of symmetry algebras extends to rigidity of the action of the symmetry on the space. This implies that the noncommutative spaces considered can be realized as star products by particular ordering prescriptions which are compatible with the symmetry. These symmetry preserving ordering prescriptions are calculated for the quantum plane and four-dimensional quantum Euclidean space. The result can be used to construct invariant Lagrangians for quantum field theory on noncommutative spaces with a deformed symmetry.

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