3,241 research outputs found
Multiple Crossover Phenomena and Scale Hopping in Two Dimensions
We study the renormalization group for nearly marginal perturbations of a
minimal conformal field theory M_p with p >> 1. To leading order in
perturbation theory, we find a unique one-parameter family of ``hopping
trajectories'' that is characterized by a staircase-like renormalization group
flow of the C-function and the anomalous dimensions and that is related to a
recently solved factorizable scattering theory. We argue that this system is
described by interactions of the form t phi_{(1,3)} - t' \phi_{(3,1)} . As a
function of the relevant parameter t, it undergoes a phase transition with new
critical exponents simultaneously governed by all fixed points M_p, M_{p-1},
..., M_3. Integrable lattice models represent different phases of the same
integrable system that are distinguished by the sign of the irrelevant
parameter t'.Comment: 20 pages, 5 figure
Large and small Density Approximations to the thermodynamic Bethe Ansatz
We provide analytical solutions to the thermodynamic Bethe ansatz equations
in the large and small density approximations. We extend results previously
obtained for leading order behaviour of the scaling function of affine Toda
field theories related to simply laced Lie algebras to the non-simply laced
case. The comparison with semi-classical methods shows perfect agreement for
the simply laced case. We derive the Y-systems for affine Toda field theories
with real coupling constant and employ them to improve the large density
approximations. We test the quality of our analysis explicitly for the
Sinh-Gordon model and the -affine Toda field theory.Comment: 19 pages Latex, 2 figure
Decay of Metastable Vacuum in Liouville Gravity
A decay of weakly metastable phase coupled to two-dimensional Liouville
gravity is considered in the semiclassical approximation. The process is
governed by the ``critical swelling'', where the droplet fluctuation favors a
gravitational inflation inside the region of lower energy phase. This
geometrical effect modifies the standard exponential suppression of the decay
rate, substituting it with a power one, with the exponent becoming very large
in the semiclassical regime. This result is compared with the power-like
behavior of the discontinuity in the specific energy of the dynamical lattice
Ising model. The last problem is far from being semiclassical, and the
corresponding exponent was found to be 3/2. This exponent is expected to govern
any gravitational decay into a vacuum without massless excitations. We
conjecture also an exact relation between the exponent in this power-law
suppression and the central charge of the stable phase.Comment: Extended version of a talk presented at XXXIII International
Conference on High Energy Physics, Moscow, July 26 - August 02, 2006. v2: few
typos corrected, a reference and an acknowledgement adde
A New Family of Diagonal Ade-Related Scattering Theories
We propose the factorizable S-matrices of the massive excitations of the
non-unitary minimal model perturbed by the operator .
The massive excitations and the whole set of two particle S-matrices of the
theory is simply related to the unitary minimal scattering theory. The
counting argument and the Thermodynamic Bethe Ansatz (TBA) are applied to this
scattering theory in order to support this interpretation. Generalizing this
result, we describe a new family of NON UNITARY and DIAGONAL -related
scattering theories. A further generalization suggests the magnonic TBA for a
large class of non-unitary \G\otimes\G/\G coset models
(\G=A_{odd},D_n,E_{6,7,8}) perturbed by , described by
non-diagonal S-matrices.Comment: 13 pages, Latex (no macros), DFUB-92-12, DFTT/30-9
Scaling Lee-Yang Model on a Sphere. I. Partition Function
Some general properties of perturbed (rational) CFT in the background metric
of symmetric 2D sphere of radius are discussed, including conformal
perturbation theory for the partition function and the large asymptotic.
The truncated conformal space scheme is adopted to treat numerically perturbed
rational CFT's in the spherical background. Numerical results obtained for the
scaling Lee-Yang model lead to the conclusion that the partition function is an
entire function of the coupling constant. Exploiting this analytic structure we
are able to describe rather precisely the ``experimental'' truncated space
data, including even the large behavior, starting only with the CFT
information and few first terms of conformal perturbation theory.Comment: Extended version of a talk presented at the NATO Advanced Research
Workshop on Statistical Field Theories, Como 18--23 June 200
First order phase transitions and integrable field theory. The dilute q-state Potts model
We consider the two-dimensional dilute q-state Potts model on its first order
phase transition surface for 0<q\leq 4. After determining the exact scattering
theory which describes the scaling limit, we compute the two-kink form factors
of the dilution, thermal and spin operators. They provide an approximation for
the correlation functions whose accuracy is illustrated by evaluating the
central charge and the scaling dimensions along the tricritical line.Comment: 21 pages, late
Rg Flows in the -Series of Minimal Cfts
Using results of the thermodynamic Bethe Ansatz approach and conformal
perturbation theory we argue that the -perturbation of a unitary
minimal -dimensional conformal field theory (CFT) in the -series of
modular invariant partition functions induces a renormalization group (RG) flow
to the next-lower model in the -series. An exception is the first model in
the series, the 3-state Potts CFT, which under the \ZZ_2-even
-perturbation flows to the tricritical Ising CFT, the second model
in the -series. We present arguments that in the -series flow
corresponding to this exceptional case, interpolating between the tetracritical
and the tricritical Ising CFT, the IR fixed point is approached from ``exactly
the opposite direction''. Our results indicate how (most of) the relevant
conformal fields evolve from the UV to the IR CFT.Comment: 30 page
Structure Constants and Conformal Bootstrap in Liouville Field Theory
An analytic expression is proposed for the three-point function of the
exponential fields in the Liouville field theory on a sphere. In the classical
limit it coincides with what the classical Liouville theory predicts. Using
this function as the structure constant of the operator algebra we construct
the four-point function of the exponential fields and verify numerically that
it satisfies the conformal bootstrap equations, i.e., that the operator algebra
thus defined is associative. We consider also the Liouville reflection
amplitude which follows explicitly from the structure constants.Comment: 31 pages, 2 Postscript figures. Important note about existing (but
unfortunately previously unknown to us) paper which has significant overlap
with this work is adde
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