311 research outputs found
Thermodynamic Bethe Ansatz and Threefold Triangulations
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 into 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 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.Comment: 17 pages, 2 eps figures, enlarged version to appear in IJMP
A topological invariant of RG flows in 2D integrable quantum field theories
We construct a topological invariant of the renormalization group
trajectories of a large class of 2D quantum integrable models, described by the
thermodynamic Bethe ansatz approach. A geometrical description of this
invariant in terms of triangulations of three-dimensional manifolds is proposed
and associated dilogarithm identities are proven.Comment: 12 pages, 6 figures. Presented at the Euroconference on New
Symmetries in Statistical Mech. and Cond. Mat. Physics, Torino, July 20-
August 1 1998. typos correcte
Dynkin TBA's
We prove a useful identity valid for all minimal S-matrices, that
clarifies the transformation of the relative thermodynamic Bethe Ansatz (TBA)
from its standard form into the universal one proposed by Al.B.Zamolodchikov.
By considering the graph encoding of the system of functional equations for the
exponentials of the pseudoenergies, we show that any such system having the
same form as those for the TBA's, can be encoded on only.
This includes, besides the known diagonal scattering, the set of all
related {\em magnonic} TBA's. We explore this class sistematically and
find some interesting new massive and massless RG flows. The generalization to
classes related to higher rank algebras is briefly presented and an intriguing
relation with level-rank duality is signalled.Comment: 29 pages, Latex (no macros) DFUB-92-11, DFTT-31/9
Complex WKB Analysis of a PT Symmetric Eigenvalue Problem
The spectra of a particular class of PT symmetric eigenvalue problems has
previously been studied, and found to have an extremely rich structure. In this
paper we present an explanation for these spectral properties in terms of
quantisation conditions obtained from the complex WKB method. In particular, we
consider the relation of the quantisation conditions to the reality and
positivity properties of the eigenvalues. The methods are also used to examine
further the pattern of eigenvalue degeneracies observed by Dorey et al. in
[1,2].Comment: 22 pages, 13 figures. Added references, minor revision
Finite size effects in perturbed boundary conformal field theories
We discuss the finite-size properties of a simple integrable quantum field
theory in 1+1 dimensions with non-trivial boundary conditions. Novel
off-critical identities between cylinder partition functions of models with
differing boundary conditions are derived.Comment: 7 pages, 11 figures, JHEP proceedings style. Uses epsfig, amssymb.
Talk given at the conference `Nonperturbative Quantum Effects 2000', Pari
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