2,208 research outputs found
Non-Local Virasoro Symmetries in the mKdV Hierarchy
We generalize the dressing symmetry construction in mKdV hierarchy. This
leads to non-local vector fields (expressed in terms of vertex operators)
closing a Virasoro algebra. We argue that this algebra realization should play
an important role in the study of 2D integrable field theories and in
particular should be related to the Deformed Virasoro Algebra (DVA) when the
construction is perturbed out of the critical theory.Comment: 11 pages, LaTex fil
Universal Amplitude Ratios of The Renormalization Group: Two-Dimensional Tricritical Ising Model
The scaling form of the free-energy near a critical point allows for the
definition of various thermodynamical amplitudes and the determination of their
dependence on the microscopic non-universal scales. Universal quantities can be
obtained by considering special combinations of the amplitudes. Together with
the critical exponents they characterize the universality classes and may be
useful quantities for their experimental identification. We compute the
universal amplitude ratios for the Tricritical Ising Model in two dimensions by
using several theoretical methods from Perturbed Conformal Field Theory and
Scattering Integrable Quantum Field Theory. The theoretical approaches are
further supported and integrated by results coming from a numerical
determination of the energy eigenvalues and eigenvectors of the off-critical
systems in an infinite cylinder.Comment: 61 pages, Latex file, figures in a separate fil
Exact conserved quantities on the cylinder II: off-critical case
With the aim of exploring a massive model corresponding to the perturbation
of the conformal model [hep-th/0211094] the nonlinear integral equation for a
quantum system consisting of left and right KdV equations coupled on the
cylinder is derived from an integrable lattice field theory. The eigenvalues of
the energy and of the transfer matrix (and of all the other local integrals of
motion) are expressed in terms of the corresponding solutions of the nonlinear
integral equation. The analytic and asymptotic behaviours of the transfer
matrix are studied and given.Comment: enlarged version before sending to jurnal, second part of
hep-th/021109
On the Integrable Structure of the Ising Model
Starting from the lattice realization of the Ising model defined on a
strip with integrable boundary conditions, the exact spectrum (including
excited states) of all the local integrals of motion is derived in the
continuum limit by means of TBA techniques. It is also possible to follow the
massive flow of this spectrum between the UV conformal fixed point and
the massive IR theory. The UV expression of the eigenstates of such integrals
of motion in terms of Virasoro modes is found to have only rational
coefficients and their fermionic representation turns out to be simply related
to the quantum numbers describing the spectrum.Comment: 18 pages, no figure
Hidden Virasoro Symmetry of (Soliton Solutions of) the Sine Gordon Theory
We present a construction of a Virasoro symmetry of the sine-Gordon (SG)
theory. It is a dynamical one and has nothing to do with the space-time
Virasoro symmetry of 2D CFT. Although it is clear how it can be realized
dyrectly in the SG field theory, we are rather concerned here with the
corresponding N-soliton solutions. We present explicit expressions for their
infinithesimal transformations and show that they are local in this case. Some
preliminary stages about the quantization of the classical results presented in
this paper are also given.Comment: 17 pages, corrected some typos, two references adde
Exact conserved quantities on the cylinder I: conformal case
The nonlinear integral equations describing the spectra of the left and right
(continuous) quantum KdV equations on the cylinder are derived from integrable
lattice field theories, which turn out to allow the Bethe Ansatz equations of a
twisted ``spin -1/2'' chain. A very useful mapping to the more common nonlinear
integral equation of the twisted continuous spin chain is found. The
diagonalization of the transfer matrix is performed. The vacua sector is
analysed in detail detecting the primary states of the minimal conformal models
and giving integral expressions for the eigenvalues of the transfer matrix.
Contact with the seminal papers \cite{BLZ, BLZ2} by Bazhanov, Lukyanov and
Zamolodchikov is realised. General expressions for the eigenvalues of the
infinite-dimensional abelian algebra of local integrals of motion are given and
explicitly calculated at the free fermion point.Comment: Journal version: references added and minor corrections performe
On the Null Vectors in the Spectra of the 2D Integrable Hierarchies
We propose an alternative description of the spectrum of local fields in the
classical limit of the integrable quantum field theories. It is close to
similar constructions used in the geometrical treatment of W-gravities. Our
approach provides a systematic way of deriving the null-vectors that appear in
this construction. We present explicit results for the case of the
A_1^{1}-(m)KdV and the A_2^{2}-(m)KdV hierarchies, different classical limits
of 2D CFT's. In the former case our results coincide with the classical limit
of the construction of Babelon, Bernard and Smirnov.Some hints about
quantization and off-critical treatment are also given.Comment: 15 pages, LATEX file, to appear in Phys.Lett.
From finite geometry exact quantities to (elliptic) scattering amplitudes for spin chains: the 1/2-XYZ
Initially, we derive a nonlinear integral equation for the vacuum counting
function of the spin 1/2-XYZ chain in the {\it disordered regime}, thus
paralleling similar results by Kl\"umper \cite{KLU}, achieved through a
different technique in the {\it antiferroelectric regime}. In terms of the
counting function we obtain the usual physical quantities, like the energy and
the transfer matrix (eigenvalues). Then, we introduce a double scaling limit
which appears to describe the sine-Gordon theory on cylindrical geometry, so
generalising famous results in the plane by Luther \cite{LUT} and Johnson et
al. \cite{JKM}. Furthermore, after extending the nonlinear integral equation to
excitations, we derive scattering amplitudes involving solitons/antisolitons
first, and bound states later. The latter case comes out as manifestly related
to the Deformed Virasoro Algebra of Shiraishi et al. \cite{SKAO}. Although this
nonlinear integral equations framework was contrived to deal with finite
geometries, we prove it to be effective for discovering or rediscovering
S-matrices. As a particular example, we prove that this unique model furnishes
explicitly two S-matrices, proposed respectively by Zamolodchikov \cite{ZAMe}
and Lukyanov-Mussardo-Penati \cite{LUK, MP} as plausible scattering description
of unknown integrable field theories.Comment: Article, 41 pages, Late
TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT
We consider high spin, , long twist, , planar operators (asymptotic
Bethe Ansatz) of strong SYM. Precisely, we compute the minimal
anomalous dimensions for large 't Hooft coupling to the lowest order
of the (string) scaling variable with GKP string size . At the leading order ,
we can confirm the O(6) non-linear sigma model description for this bulk term,
without boundary term . Going further, we derive,
extending the O(6) regime, the exact effect of the size finiteness. In
particular, we compute, at all loops, the first Casimir correction (in terms of the infinite size O(6) NLSM), which reveals only one
massless mode (out of five), as predictable once the O(6) description has been
extended. Consequently, upon comparing with string theory expansion, at one
loop our findings agree for large twist, while reveal for negligible twist,
already at this order, the appearance of wrapping. At two loops, as well as for
next loops and orders, we can produce predictions, which may guide future
string computations.Comment: Version 2 with: new exact expression for the Casimir energy derived
(beyond the first two loops of the previous version); UV theory formulated
and analysed extensively in the Appendix C; origin of the O(6) NLSM
scattering clarified; typos correct and references adde
Integrability and cycles of deformed N=2 gauge theory
To analyse pure N=2 SU(2) gauge theory in the Nekrasov-Shatashvili (NS) limit (or deformed Seiberg-Witten (SW)), we use the Ordinary Differential Equation/Integrable Model (ODE/IM) correspondence, and in particular its (broken) discrete symmetry in its extended version with two singular irregular points. Actually, this symmetry appears to be ‘manifestation’ of the spontaneously broken Z2 R-symmetry of the original gauge problem and the two deformed SW one-cycle periods are simply connected to the Baxter's T and Q functions, respectively, of the Liouville conformal field theory at the self-dual point. The liaison is realised via a second order differential operator which is essentially the ‘quantum’ version of the square of the SW differential. Moreover, the constraints imposed by the broken Z2 R-symmetry acting on the moduli space (Bilal-Ferrari equations) seem to have their quantum counterpart in the TQ and the T periodicity relations, and integrability yields also a useful Thermodynamic Bethe Ansatz (TBA) for the periods (Y(θ,±u) or their square roots, Q(θ,±u)). A latere, two efficient asymptotic expansion techniques are presented. Clearly, the whole construction is extendable to gauge theories with matter and/or higher rank groups
- …