1,990 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 $R$ are discussed, including conformal
perturbation theory for the partition function and the large $R$ 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 $R$ 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

### On two-dimensional quantum gravity and quasiclassical integrable hierarchies

The main results for the two-dimensional quantum gravity, conjectured from
the matrix model or integrable approach, are presented in the form to be
compared with the world-sheet or Liouville approach. In spherical limit the
integrable side for minimal string theories is completely formulated using
simple manipulations with two polynomials, based on residue formulas from
quasiclassical hierarchies. Explicit computations for particular models are
performed and certain delicate issues of nontrivial relations among them are
discussed. They concern the connections between different theories, obtained as
expansions of basically the same stringy solution to dispersionless KP
hierarchy in different backgrounds, characterized by nonvanishing background
values of different times, being the simplest known example of change of the
quantum numbers of physical observables, when moving to a different point in
the moduli space of the theory.Comment: 20 pages, based on talk presented at the conference "Liouville field
theory and statistical models", dedicated to the memory of Alexei
Zamolodchikov, Moscow, June 200

### N=1 SUSY Conformal Block Recursive Relations

We present explicit recursive relations for the four-point superconformal
block functions that are essentially particular contributions of the given
conformal class to the four-point correlation function. The approach is based
on the analytic properties of the superconformal blocks as functions of the
conformal dimensions and the central charge of the superconformal algebra. The
results are compared with the explicit analytic expressions obtained for
special parameter values corresponding to the truncated operator product
expansion. These recursive relations are an efficient tool for numerically
studying the four-point correlation function in Super Conformal Field Theory in
the framework of the bootstrap approach, similar to that in the case of the
purely conformal symmetry.Comment: 12 pages, typos corrected, reference 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 $M_{2,11}$ perturbed by the operator $\Phi_{1,4}$.
The massive excitations and the whole set of two particle S-matrices of the
theory is simply related to the $E_8$ 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 $ADE$-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 $\Phi_{id,id,adj}$, 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 $(G_2^{(1)},D_4^{(3)})$-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.

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