ON THE BREATHERS OF $a_n^{(1)} $ AFFINE TODA FIELD THEORY

Harder, Uli; Iskandar, Alexander A.; McGhee, William A

doi:10.1142/s0217751x95000917

Cited by 13 publications

(25 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It should also be noted that, as already discovered in the a (1) 2 case [18] and for the classical solitons of a (1) n AFTF [6], only fundamental solitons of the same species (and of conjugate species in non-self-conjugate theories) can form bound states (figures 5b and 5c). We expect this to be a common feature of all imaginary ATFTs.…”

supporting

confidence: 61%

Exact S-matrices for d(2)n+1 affine Toda solitons and their bound states

Gandenberger

MacKay

1995

Nuclear Physics B

View full text Add to dashboard Cite

We conjecture an exact S-matrix for the scattering of solitons in d(2) n+1 affine Toda field theory in terms of the R-matrix of the quantum group U q (c (1) n ). From this we construct the scattering amplitudes for all scalar bound states (breathers) of the theory. This S-matrix conjecture is justified by detailed examination of its pole structure. We show that a breather-particle identification holds by comparing the S-matrix elements for the lowest breathers with the S-matrix for the quantum particles in real affine Toda field theory, and discuss the implications for various forms of duality.

show abstract

supporting

confidence: 61%

Exact S-matrices for d(2)n+1 affine Toda solitons and their bound states

Gandenberger

MacKay

1995

Nuclear Physics B

View full text Add to dashboard Cite

show abstract

“…agrees with the "type A breather" of [29], see the equation following Eq. (4.17) of that work, provided we choose ρ ′ = ρ and certain relations among σ a , A, v and θ a .…”

Section: Comparison With Other Work and Outlooksupporting

confidence: 66%

“…We were not able to generate "type B breathers" of Ref. [29] at all with our methods. On the other hand, we have more freedom in constructing more complicated breather candidates by allowing for diagonal elements of ω.…”

Section: Comparison With Other Work and Outlookmentioning

confidence: 92%

SU(N) affine Toda solitons and breathers from transparent Dirac potentials

Thies¹

2017

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

Transparent scalar and pseudoscalar potentials in the one-dimensional Dirac equation play an important role as self-consistent mean fields in 1+1 dimensional four-fermion theories (Gross-Neveu, Nambu-Jona Lasinio models) and quasi-one dimensional superconductors (Bogoliubov-De Gennes equation). Here, we show that they also serve as seed to generate a large class of classical multisoliton and multi-breather solutions of su(N ) affine Toda field theories, including the Lax representation and the corresponding vector. This generalizes previous findings about the relationship between real kinks in the Gross-Neveu model and classical solitons of the sinh-Gordon equation to complex twisted kinks.

show abstract

“…All the known soliton solutions of the a (1) n Toda theories were found by Hollowood in [28], the breathers by Harder et al in [29], and the scattering of solitons by Olive et al in [30]. We take the action of a…”

Section: The S-matrices For Soliton-breather Scattering In Amentioning

confidence: 99%

Non-unitarity in quantum affine Toda theory and perturbed conformal field theory

Takács

Watts

1999

Nuclear Physics B

View full text Add to dashboard Cite

There has been some debate about the validity of quantum affine Toda field theory at imaginary coupling, owing to the non-unitarity of the action, and consequently of its usefulness as a model of perturbed conformal field theory. Drawing on our recent work, we investigate the two simplest affine Toda theories for which this is an issue -a (1) 2 and a (2) 2 . By investigating the S-matrices of these theories before RSOS restriction, we show that quantum Toda theory, (with or without RSOS restriction), indeed has some fundamental problems, but that these problems are of two different sorts. For a (1) 2 , the scattering of solitons and breathers is flawed in both classical and quantum theories, and RSOS restriction cannot solve this problem. For a (2) 2 however, while there are no problems with breather-soliton scattering there are instead difficulties with soliton-excited soliton scattering in the unrestricted theory. After RSOS restriction, the problems with kink-excited kink may be cured or may remain, depending in part on the choice of gradation, as we found in [12]. We comment on the importance of regradations, and also on the survival of R-matrix unitarity and the S-matrix bootstrap in these circumstances.

show abstract

ON THE BREATHERS OF $a_n^{(1)} $ AFFINE TODA FIELD THEORY

Cited by 13 publications

References 20 publications

Exact S-matrices for d(2)n+1 affine Toda solitons and their bound states

Exact S-matrices for d(2)n+1 affine Toda solitons and their bound states

SU(N) affine Toda solitons and breathers from transparent Dirac potentials

Non-unitarity in quantum affine Toda theory and perturbed conformal field theory

Contact Info

Product

Resources

About