506 research outputs found
Recursive representation of the torus 1-point conformal block
The recursive relation for the 1-point conformal block on a torus is derived
and used to prove the identities between conformal blocks recently conjectured
by R. Poghossian. As an illustration of the efficiency of the recurrence method
the modular invariance of the 1-point Liouville correlation function is
numerically analyzed.Comment: 14 pages, 1 eps figure, misprints corrected and a reference adde
Field theory of scaling lattice models. The Potts antiferromagnet
In contrast to what happens for ferromagnets, the lattice structure
participates in a crucial way to determine existence and type of critical
behaviour in antiferromagnetic systems. It is an interesting question to
investigate how the memory of the lattice survives in the field theory
describing a scaling antiferromagnet. We discuss this issue for the square
lattice three-state Potts model, whose scaling limit as T->0 is argued to be
described exactly by the sine-Gordon field theory at a specific value of the
coupling. The solution of the scaling ferromagnetic case is recalled for
comparison. The field theory describing the crossover from antiferromagnetic to
ferromagnetic behaviour is also introduced.Comment: 11 pages, to appear in the proceedings of the NATO Advanced Research
Workshop on Statistical Field Theories, Como 18-23 June 200
On O(1) contributions to the free energy in Bethe Ansatz systems: the exact g-function
We investigate the sub-leading contributions to the free energy of Bethe
Ansatz solvable (continuum) models with different boundary conditions. We show
that the Thermodynamic Bethe Ansatz approach is capable of providing the O(1)
pieces if both the density of states in rapidity space and the quadratic
fluctuations around the saddle point solution to the TBA are properly taken
into account. In relativistic boundary QFT the O(1) contributions are directly
related to the exact g-function. In this paper we provide an all-orders proof
of the previous results of P. Dorey et al. on the g-function in both massive
and massless models. In addition, we derive a new result for the g-function
which applies to massless theories with arbitrary diagonal scattering in the
bulk.Comment: 28 pages, 2 figures, v2: minor corrections, v3: minor corrections and
references adde
Quantum Sine(h)-Gordon Model and Classical Integrable Equations
We study a family of classical solutions of modified sinh-Gordon equation,
$\partial_z\partial_{{\bar z}} \eta-\re^{2\eta}+p(z)\,p({\bar z})\
\re^{-2\eta}=0p(z)=z^{2\alpha}-s^{2\alpha}Q(\alpha>0)(\alpha<-1)$ models.Comment: 35 pages, 3 figure
Correlation Functions in 2-Dimensional Integrable Quantum Field Theories
In this talk I discuss the form factor approach used to compute correlation
functions of integrable models in two dimensions. The Sinh-Gordon model is our
basic example. Using Watson's and the recursive equations satisfied by matrix
elements of local operators, I present the computation of the form factors of
the elementary field and the stress-energy tensor of
the theory.Comment: 19pp, LATEX version, (talk at Como Conference on ``Integrable Quantum
Field Theories''
Scattering and duality in the 2 dimensional OSP(2|2) Gross Neveu and sigma models
We write the thermodynamic Bethe ansatz for the massive OSp(2|2) Gross Neveu
and sigma models. We find evidence that the GN S matrix proposed by Bassi and
Leclair [12] is the correct one. We determine features of the sigma model S
matrix, which seem highly unconventional; we conjecture in particular a
relation between this sigma model and the complex sine-Gordon model at a
particular value of the coupling. We uncover an intriguing duality between the
OSp(2|2) GN (resp. sigma) model on the one hand, and the SO(4) sigma (resp. GN
model) on the other, somewhat generalizing to the massive case recent results
on OSp(4|2). Finally, we write the TBA for the (SUSY version of the) flow into
the random bond Ising model proposed by Cabra et al. [39], and conclude that
their S matrix cannot be correct.Comment: 41 pages, 27 figures. v2: minor revisio
Integrable Boundary Conditions for the O(N) Nonlinear Model
We discuss the new integrable boundary conditions for the O(N) nonlinear
model and related solutions of the boundary Yang-Baxter equation,
which were presented in our previous paper hep-th/0108039.Comment: 9 pages. To appear in the proceedings of the NATO Advanced Research
Workshop on "Statistical Field Theories", Como, Italy, 18-23 June 2001. v2:
typos correcte
Conformal Toda theory with a boundary
We investigate sl(n) conformal Toda theory with maximally symmetric
boundaries. There are two types of maximally symmetric boundary conditions, due
to the existence of an order two automorphism of the W(n>2) algebra. In one of
the two cases, we find that there exist D-branes of all possible dimensions 0
=< d =< n-1, which correspond to partly degenerate representations of the W(n)
algebra. We perform classical and conformal bootstrap analyses of such
D-branes, and relate these two approaches by using the semi-classical light
asymptotic limit. In particular we determine the bulk one-point functions. We
observe remarkably severe divergences in the annulus partition functions, and
attribute their origin to the existence of infinite multiplicities in the
fusion of representations of the W(n>2) algebra. We also comment on the issue
of the existence of a boundary action, using the calculus of constrained
functional forms, and derive the generating function of the B"acklund
transformation for sl(3) Toda classical mechanics, using the minisuperspace
limit of the bulk one-point function.Comment: 42 pages; version 4: added clarifications in section 2.2 and
footnotes 1 and
Form factors at strong coupling via a Y-system
We compute form factors in planar N=4 Super Yang-Mills at strong coupling.
Namely we consider the overlap between an operator insertion and 2n gluons.
Through the gauge/string duality these are given by minimal surfaces in AdS
space. The surfaces end on an infinite periodic sequence of null segments at
the boundary of AdS. We consider surfaces that can be embedded in AdS_3. We
derive set of functional equations for the cross ratios as functions of the
spectral parameter. These equations are of the form of a Y-system. The integral
form of the Y-system has Thermodynamics Bethe Ansatz form. The area is given by
the free energy of the TBA system or critical value of Yang-Yang functional. We
consider a restricted set of operators which have small conformal dimension
One-point functions in massive integrable QFT with boundaries
We consider the expectation value of a local operator on a strip with
non-trivial boundaries in 1+1 dimensional massive integrable QFT. Using finite
volume regularisation in the crossed channel and extending the boundary state
formalism to the finite volume case we give a series expansion for the
one-point function in terms of the exact form factors of the theory. The
truncated series is compared with the numerical results of the truncated
conformal space approach in the scaling Lee-Yang model. We discuss the
relevance of our results to quantum quench problems.Comment: 43 pages, 20 figures, v2: typos correcte
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