Non-Linear Integral Equations for complex Affine Toda associated to simply laced Lie algebras

P. Zinn-Justin

doi:10.1088/0305-4470/31/31/019

Non-Linear Integral Equations for complex Affine Toda associated to simply laced Lie algebras

High Energy Physics - Theory 2008-11-26 v5 Exactly Solvable and Integrable Systems solv-int

Authors: P. Zinn-Justin

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Abstract

A set of coupled non-linear integral equations is derived for a class of models connected with the quantum group $U_q(\hat g)$ ( $g$ simply laced Lie algebra), which are solvable using the Bethe Ansatz; these equations describe arbitrary excited states of a system with finite spatial length $L$ . They generalize the Destri-De Vega equation for the Sine-Gordon/massive Thirring model to affine Toda field theory with imaginary coupling constant. As an application, the central charge and all the conformal weights of the UV conformal field theory are extracted in a straightforward manner. The quantum group truncation for $q$ at a root of unity is discussed in detail; in the UV limit we recover through this procedure the RCFTs with extended $W(g)$ conformal symmetry.

Keywords

non-linear integral equations affine Toda field theory quantum group Bethe ansatz conformal field theory UV limit

Cite

@article{arxiv.hep-th/9712222,
  title  = {Non-Linear Integral Equations for complex Affine Toda associated to simply laced Lie algebras},
  author = {P. Zinn-Justin},
  journal= {arXiv preprint arXiv:hep-th/9712222},
  year   = {2008}
}

Comments

33 pages, TeX with lanlmac (revised: minor misprints corrected, some comments added, appendix slightly expanded revised 05/98: more misprints corrected, important refs added)

Non-Linear Integral Equations for complex Affine Toda associated to simply laced Lie algebras

Abstract

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