185 research outputs found
Finite size effects in quantum field theories with boundary from scattering data
We derive a relation between leading finite size corrections for a 1+1
dimensional quantum field theory on a strip and scattering data, which is very
similar in spirit to the approach pioneered by Luscher for periodic boundary
conditions. The consistency of the results is tested both analytically and
numerically using thermodynamic Bethe Ansatz, Destri-de Vega nonlinear integral
equation and classical field theory techniques. We present strong evidence that
the relation between the boundary state and the reflection factor one-particle
couplings, noticed earlier by Dorey et al. in the case of the Lee-Yang model
extends to any boundary quantum field theory in 1+1 dimensions.Comment: 24 pages, 1 eps figure. Clarifying comments and a reference adde
A2 Toda theory in reduced WZNW framework and the representations of the W algebra
Using the reduced WZNW formulation we analyse the classical orbit content
of the space of classical solutions of the Toda theory. We define the
quantized Toda field as a periodic primary field of the algebra satisfying
the quantized equations of motion. We show that this local operator can be
constructed consistently only in a Hilbert space consisting of the
representations corresponding to the minimal models of the algebra.Comment: 38 page
Explicit boundary form factors: the scaling Lee-Yang model
We provide explicit expressions for boundary form factors in the boundary
scaling Lee-Yang model for operators with the mildest ultraviolet behavior for
all integrable boundary conditions. The form factors of the boundary stress
tensor take a determinant form, while the form factors of the boundary primary
field contain additional explicit polynomials.Comment: 18 pages, References adde
Boundary one-point function, Casimir energy and boundary state formalism in D+1 dimensional QFT
We consider quantum field theories with boundary on a codimension one
hyperplane. Using 1+1 dimensional examples, we clarify the relation between
three parameters characterising one-point functions, finite size corrections to
the ground state energy and the singularity structure of scattering amplitudes,
respectively. We then develop the formalism of boundary states in general D+1
spacetime dimensions and relate the cluster expansion of the boundary state to
the correlation functions using reduction formulae. This allows us to derive
the cluster expansion in terms of the boundary scattering amplitudes, and to
give a derivation of the conjectured relations between the parameters in 1+1
dimensions, and their generalization to D+1 dimensions. We use these results to
express the large volume asymptotics of the Casimir effect in terms of the
one-point functions or alternatively the singularity structure of the
one-particle reflection factor, and for the case of vanishing one-particle
couplings we give a complete proof of our previous result for the leading
behaviour.Comment: 32 pages, 1 eps figure
On the boundary form factor program
Boundary form factor axioms are derived for the matrix elements of local
boundary operators in integrable 1+1 dimensional boundary quantum field
theories using the analyticity properties of correlators via the boundary
reduction formula. Minimal solutions are determined for the integrable boundary
perturbations of the free boson, free fermion (Ising), Lee-Yang and sinh-Gordon
models and the two point functions calculated from them are checked against the
exact solutions in the free cases and against the conformal data in the
ultraviolet limit for the Lee-Yang model. In the case of the free boson/fermion
the dimension of the solution space of the boundary form factor equation is
shown to match the number of independent local operators. We obtain excellent
agreement which proves not only the correctness of the solutions but also
confirms the form factor axioms.Comment: 38 pages, 17 eps figures, LaTeX, References adde
Finite volume form factors in the presence of integrable defects
We developed the theory of finite volume form factors in the presence of
integrable defects. These finite volume form factors are expressed in terms of
the infinite volume form factors and the finite volume density of states and
incorporate all polynomial corrections in the inverse of the volume. We tested
our results, in the defect Lee-Yang model, against numerical data obtained by
truncated conformal space approach (TCSA), which we improved by renormalization
group methods adopted to the defect case. To perform these checks we determined
the infinite volume defect form factors in the Lee-Yang model exactly,
including their vacuum expectation values. We used these data to calculate the
two point functions, which we compared, at short distance, to defect CFT. We
also derived explicit expressions for the exact finite volume one point
functions, which we checked numerically. In all of these comparisons excellent
agreement was found.Comment: pdflatex, 34 pages, many 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
Scaling function in AdS/CFT from the O(6) sigma model
Asymptotic behavior of the anomalous dimensions of Wilson operators with high
spin and twist is governed in planar N=4 SYM theory by the scaling function
which coincides at strong coupling with the energy density of a two-dimensional
bosonic O(6) sigma model. We calculate this function by combining the two-loop
correction to the energy density for the O(n) model with two-loop correction to
the mass gap determined by the all-loop Bethe ansatz in N=4 SYM theory. The
result is in agreement with the prediction coming from the thermodynamical
limit of the quantum string Bethe ansatz equations, but disagrees with the
two-loop stringy corrections to the folded spinning string solution.Comment: 25 pages, 2 figure
Geometry of W-algebras from the affine Lie algebra point of view
To classify the classical field theories with W-symmetry one has to classify
the symplectic leaves of the corresponding W-algebra, which are the
intersection of the defining constraint and the coadjoint orbit of the affine
Lie algebra if the W-algebra in question is obtained by reducing a WZNW model.
The fields that survive the reduction will obey non-linear Poisson bracket (or
commutator) relations in general. For example the Toda models are well-known
theories which possess such a non-linear W-symmetry and many features of these
models can only be understood if one investigates the reduction procedure. In
this paper we analyze the SL(n,R) case from which the so-called W_n-algebras
can be obtained. One advantage of the reduction viewpoint is that it gives a
constructive way to classify the symplectic leaves of the W-algebra which we
had done in the n=2 case which will correspond to the coadjoint orbits of the
Virasoro algebra and for n=3 which case gives rise to the Zamolodchikov
algebra. Our method in principle is capable of constructing explicit
representatives on each leaf. Another attractive feature of this approach is
the fact that the global nature of the W-transformations can be explicitly
described. The reduction method also enables one to determine the ``classical
highest weight (h. w.) states'' which are the stable minima of the energy on a
W-leaf. These are important as only to those leaves can a highest weight
representation space of the W-algebra be associated which contains a
``classical h. w. state''.Comment: 17 pages, LaTeX, revised 1. and 7. chapter
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