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.

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.

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.

ELASTIC S-MATRICES IN (1 + 1) DIMENSIONS AND TODA FIELD THEORIES

1990 ◽  
Vol 05 (24) ◽  
pp. 4581-4627 ◽  
Author(s):  
P. CHRISTE ◽  
G. MUSSARDO
Keyword(s):  
Field Theory ◽  
General Scheme ◽  
Field Theories ◽  
Scattering Data ◽  
Quantum Field Theories ◽  
Conformal Field ◽  
Dynkin Diagrams ◽  
S Matrix ◽  
Relativistic Scattering ◽  
Toda Field Theory

Particular deformations of 2-D conformal field theory lead to integrable massive quantum field theories. These can be characterized by the relativistic scattering data. We propose a general scheme for classifying the elastic nondegenerate S-matrix in (1 + 1) dimensions starting from the possible boot-strap processes and the spins of the conserved currents. Their identification with the S-matrix coming from the Toda field theory is analyzed. We discuss both cases of Toda field theory constructed with the simply-laced Dynkin diagrams and the nonsimply-laced ones. We present the results of the perturbative analysis and their geometrical interpretations.

The Other Einstein: Einstein Contra Field Theory

1993 ◽  
Vol 6 (1) ◽  
pp. 275-290 ◽  
Author(s):  
John Stachel
Keyword(s):  
Field Theory ◽  
The Other ◽  
Field Theories ◽  
Unified Field Theories ◽  
Unified Field ◽  
The Continuum

The ArgumentBesides the well-known advocate of unified field theories, there was “another Einstein,” who was skeptical of the continuum as a foundational element in physics. This paper presents evidence for the existence of this “other Einstein,” and of the debate between the two Einsteins that lasted most of Einstein's life.

scholarly journals ON FIELD THEORIES OF LOOPS

1995 ◽  
Vol 10 (29) ◽  
pp. 2175-2184 ◽  
Author(s):  
NAOHITO NAKAZAWA
Keyword(s):  
Field Theory ◽  
Stochastic Process ◽  
Loop Space ◽  
Continuum Limit ◽  
Symmetric Matrix ◽  
Field Theories ◽  
Stochastic Quantization ◽  
Quantization Method ◽  
Second Quantization ◽  
The Continuum

We apply stochastic quantization method to real symmetric matrix models for the second quantization of nonorientable loops in both discretized and continuum levels. The stochastic process defined by the Langevin equation in loop space describes the time evolution of the nonorientable loops defined on nonorientable 2-D surfaces. The corresponding Fokker-Planck Hamiltonian deduces a nonorientable string field theory at the continuum limit.

scholarly journals SOME REMARKS ON D-BRANES AND DEFECTS IN LIOUVILLE AND TODA FIELD THEORIES

2012 ◽  
Vol 27 (31) ◽  
pp. 1250181 ◽  
Author(s):  
GOR SARKISSIAN
Keyword(s):  
Field Theory ◽  
Simple Form ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
General Properties ◽  
Boundary States ◽  
Toda Field Theory

In this paper, we analyze the Cardy–Lewellen equation in general diagonal model. We show that in these models it takes a simple form due to some general properties of conformal field theories, like pentagon equations and OPE associativity. This implies that the Cardy–Lewellen equation has a simple form also in nonrational diagonal models. We specialize our finding to the Liouville and Toda field theories. In particular, we prove that recently conjectured defects in Toda field theory indeed satisfy the cluster equation. We also derive the Cardy–Lewellen equation in all sl(n) Toda field theories and prove that the form of boundary states found recently in sl(3) Toda field theory holds in all sl(n) theories as well.

scholarly journals FREE FIELD REPRESENTATION OF TODA FIELD THEORIES

1994 ◽  
Vol 09 (01) ◽  
pp. 57-86 ◽  
Author(s):  
E. ALDROVANDI ◽  
L. BONORA ◽  
V. BONSERVIZI ◽  
R. PAUNOV
Keyword(s):  
Field Theory ◽  
Free Field ◽  
Field Theories ◽  
Singular Solutions ◽  
Field Equations ◽  
Field Representation ◽  
Zero Modes ◽  
Free Left ◽  
Left And Right ◽  
Toda Field Theory

We study the following problem: Can a classical sl n Toda field theory be represented by means of free bosonic oscillators through a Drinfeld-Sokolov construction? We answer affirmatively in the case of a cylindrical space-time and for real hyperbolic solutions of the Toda field equations. We establish in fact a one-to-one correspondence between such solutions and the space of free left and right bosonic oscillators with coincident zero modes. We discuss the same problem for real singular solutions with nonhyperbolic monodromy.

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