197 research outputs found
On the renormalisation group for the boundary Truncated Conformal Space Approach
In this paper we continue the study of the truncated conformal space approach
to perturbed boundary conformal field theories. This approach to perturbation
theory suffers from a renormalisation of the coupling constant and a
multiplicative renormalisation of the Hamiltonian. We show how these two
effects can be predicted by both physical and mathematical arguments and prove
that they are correct to leading order for all states in the TCSA system. We
check these results using the TCSA applied to the tri-critical Ising model and
the Yang-Lee model. We also study the TCSA of an irrelevant
(non-renormalisable) perturbation and find that, while the convergence of the
coupling constant and energy scales are problematic, the renormalised and
rescaled spectrum remain a very good fit to the exact result, and we find a
numerical relationship between the IR and UV couplings describing a particular
flow. Finally we study the large coupling behaviour of TCSA and show that it
accurately encompasses several different fixed points.Comment: 27 pages, 19 figure
Integrals of motion from TBA and lattice-conformal dictionary
The integrals of motion of the tricritical Ising model are obtained by
Thermodynamic Bethe Ansatz (TBA) equations derived from the A_4 integrable
lattice model. They are compared with those given by the conformal field theory
leading to a unique one-to-one lattice-conformal correspondence. They can also
be followed along the renormalization group flows generated by the action of
the boundary field \phi_{1,3} on conformal boundary conditions in close analogy
to the usual TBA description of energies.Comment: 20 pages, 1 figure, LaTeX; v2: added references, improved conventions
introduced in sections 4, 5 and related tables; v3: added reference
Finite volume spectrum of N=1 superminimal models perturbed by
We describe an extension of the nonlinear integral equation (NLIE) tehnique
to N=1 superminimal models perturbed by . Along the way, we also
complete our previous studies of the finite volume spectrum of the N=1
supersymmetric sine-Gordon model by considering the attractive regime and more
specifically, breather states
Scaling Functions in the Odd Charge Sector of Sine-Gordon/Massive Thirring Theory
A non-linear integral equation (NLIE) governing the finite size effects of
excited states of even topological charge in the sine-Gordon (sG) / massive
Thirring (mTh) field theory, deducible from a light-cone lattice formulation of
the model, has been known for some time. In this letter we conjecture an
extension of this NLIE to states with odd topological charge, thus completing
the spectrum of the theory. The scaling functions obtained as solutions to our
conjectured NLIE are compared successfully with Truncated Conformal Space data
and the construction is shown to be compatible with all other facts known about
the local Hilbert spaces of sG and mTh models. With the present results we have
achieved a full control over the finite size behaviour of energy levels of
sG/mTh theory.Comment: LaTeX2e, 12 pp., 3 eps figs. Remarks on locality adde
On the finite size corrections of anti-ferromagnetic anomalous dimensions in SYM
Non-linear integral equations derived from Bethe Ansatz are used to evaluate
finite size corrections to the highest (i.e. {\it anti-ferromagnetic}) and
immediately lower anomalous dimensions of scalar operators in SYM.
In specific, multi-loop corrections are computed in the SU(2) operator
subspace, whereas in the general SO(6) case only one loop calculations have
been finalised. In these cases, the leading finite size corrections are given
by means of explicit formul\ae and compared with the exact numerical
evaluation. In addition, the method here proposed is quite general and
especially suitable for numerical evaluations.Comment: 38 pages, Latex revised version: draft formulae indicator deleted,
one reference added, typos corrected, few minor text modification
Finite Volume Spectrum of Sine-Gordon Model and its Restrictions
In this thesis, we review recent progresses on Nonlinear Integral Equation
approach to finite size effects in two dimensional integrable quantum field
theories, with emphasis to Sine-Gordon/Massive Thirring model and restrictions
to minimal models perturbed by . Exact calculations of the
dependence of energy levels on the size are presented for vacuum and many
excited states.Comment: PhD thesis, 96 pages, 28 figure
Nonperturbative study of the two-frequency sine-Gordon model
The two-frequency sine-Gordon model is examined. The focus is mainly on the
case when the ratio of the frequencies is 1/2, given the recent interest in the
literature. We discuss the model both in a perturbative (form factor
perturbation theory) and a nonperturbative (truncated conformal space approach)
framework, and give particular attention to a phase transition conjectured
earlier by Delfino and Mussardo. We give substantial evidence that the
transition is of second order and that it is in the Ising universality class.
Furthermore, we check the UV-IR operator correspondence and conjecture the
phase diagram of the theory.Comment: Minor corrections, LaTeX2e, 39 pages, 26 figures (4 pslatex, 1
postscript and 21 eps
Critical RSOS and Minimal Models II: Building Representations of the Virasoro Algebra and Fields
We consider sl(2) minimal conformal field theories and the dual parafermion
models. Guided by results for the critical A_L Restricted Solid-on-Solid (RSOS)
models and its Virasoro modules expressed in terms of paths, we propose a
general level-by-level algorithm to build matrix representations of the
Virasoro generators and chiral vertex operators (CVOs). We implement our scheme
for the critical Ising, tricritical Ising, 3-state Potts and Yang-Lee theories
on a cylinder and confirm that it is consistent with the known two-point
functions for the CVOs and energy-momentum tensor. Our algorithm employs a
distinguished basis which we call the L_1-basis. We relate the states of this
canonical basis level-by-level to orthonormalized Virasoro states
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