180 research outputs found
Zamalodchikov's C-Theorem and The Logarithmic Conformal Field Theory
We consider perturbation of a conformal field theory by a pair of relevant
logarithmic operators and calculate the beta function up to two loops. We
observe that the beta function can not be derived from a potential. Thus the
renormalization group trajectories are not always along decreasing values of
the central charge. However there exists a domain of structure constants in
which the c-theorem still holds.Comment: 10 pages, latex, no figures, some references are added, The role of
coefficients of the OPE in LCFT on the beta-functions are disscuse
The Logarithmic Conformal Field Theories
We study the correlation functions of logarithmic conformal field theories.
First, assuming conformal invariance, we explicitly calculate two-- and three--
point functions. This calculation is done for the general case of more than one
logarithmic field in a block, and more than one set of logarithmic fields. Then
we show that one can regard the logarithmic field as a formal derivative of the
ordinary field with respect to its conformal weight. This enables one to
calculate any -- point function containing the logarithmic field in terms of
ordinary --point functions. At last, we calculate the operator product
expansion (OPE) coefficients of a logarithmic conformal field theory, and show
that these can be obtained from the corresponding coefficients of ordinary
conformal theory by a simple derivation.Comment: 17 pages ,latex , some minor changes, to appear in Nucl. Phys.
Logarithmic N=1 superconformal field theories
We study the logarithmic superconformal field theories. Explicitly, the
two-point functions of N=1 logarithmic superconformal field theories (LSCFT)
when the Jordan blocks are two (or more) dimensional, and when there are one
(or more) Jordan block(s) have been obtained. Using the well known three-point
fuctions of N=1 superconformal field theory (SCFT), three-point functions of
N=1 LSCFT are obtained. The general form of N=1 SCFT's four-point functions is
also obtained, from which one can easily calculate four-point functions in N=1
LSCFT.Comment: 10 pages, LaTeX file, minor revisions made, to appear in Phys. Lett.
Logarithmic Correlation Functions in Two Dimensional Turbulence
We consider the correlation functions of two-dimensional turbulence in the
presence and absence of a three-dimensional perturbation, by means of conformal
field theory. In the persence of three dimensional perturbation, we show that
in the strong coupling limit of a small scale random force, there is some
logarithmic factor in the correlation functions of velocity stream functions.
We show that the logarithmic conformal field theory describes the 2D-
turbulence both in the absence and the presence of the perturbation. We obtain
the following energy spectrum for perturbed 2D
- turbulence and for unperturbed turbulence. Recent
numerical simulation and experimental results confirm our prediction.Comment: 14 pages ,latex , no figure
Quenched Averaged Correlation Functions of the Random Magnets
It is shown that the ratios of the quenched averaged three and four-point
correlation functions of the local energy density operator to the connected
ones in the random-bond Ising model approach asymptotically to some
functions. We derive the explicit expressions of these universal functions.
Moreover it is shown that the individual logarithmic operators have not any
contribution to the connected correlation functions of the disordered Ising
model.Comment: 4 pages, twocolumn, to appear in Nucl. Physics
Phase Transition in a Self--Gravitating Planar Gas
We consider a gas of Newtonian self-gravitating particles in two-dimensional
space, finding a phase transition, with a high temperature homogeneous phase
and a low temperature clumped one. We argue that the system is described in
terms of a gas with fractal behaviour.Comment: corrections made and discussions enlarged; to appear P.L.
Global Conformal Invariance in D-dimensions and Logarithmic Correlation Functions
We define transformation of multiplets of fields (Jordan cells) under the
D-dimensional conformal group, and calculate two and three point functions of
fields, which show logarithmic behaviour. We also show how by a formal
differentiation procedure, one can obtain n-point function of logarithmic field
theory from those of ordinary conformal field theory.Comment: 9 pages, LaTeX, some misprints are corrected, to be published in
Phys. Lett.
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