1,680 research outputs found
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
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
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
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
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
Information geometric approach to the renormalisation group
We propose a general formulation of the renormalisation group as a family of
quantum channels which connect the microscopic physical world to the observable
world at some scale. By endowing the set of quantum states with an
operationally motivated information geometry, we induce the space of
Hamiltonians with a corresponding metric geometry. The resulting structure
allows one to quantify information loss along RG flows in terms of the
distinguishability of thermal states. In particular, we introduce a family of
functions, expressible in terms of two-point correlation functions, which are
non increasing along the flow. Among those, we study the speed of the flow, and
its generalization to infinite lattices.Comment: Accepted in Phys. Rev.
- âŠ