1,100 research outputs found
On the AdS/CFT Correspondence and Logarithmic Operator
Logarithmic conformal field theory is investigated using the AdS/CFT
correspondence and a novel method based on nilpotent weights. Using this device
we add ghost fermions and point to a BRST invariance of the theory.Comment: 8 Pages, Typos corrected, references added changes in the content of
the last sectio
Disordered Dirac Fermions: Multifractality Termination and Logarithmic Conformal Field Theories
We reexamine in detail the problem of fermions interacting with a non-Abelian
random vector potential. Without resorting to the replica or supersymmetry
approaches, we show that in the limit of infinite disorder strength the theory
possesses an exact solution which takes the form of a logarithmic conformal
field theory. We show that the proper treatment of the locality conditions in
the SU(2) theory leads to the termination of the multifractal spectrum, or in
other words to the termination of the infinite hierarchies of
negative-dimensional operators that were thought to occur. Based on arguments
of logarithmic degeneracies, we conjecture that such a termination mechanism
should be present for general SU(N). Moreover, our results lead to the
conclusion that the previous replica solution of this problem yields incorrect
results.Comment: Revised version, to appear in Nucl. Phys.
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
Continuously Crossing u=z in the H3+ Boundary CFT
For AdS boundary conditions, we give a solution of the H3+ two point function
involving degenerate field with SL(2)-label b^{-2}/2, which is defined on the
full (u,z) unit square. It consists of two patches, one for z<u and one for
u<z. Along the u=z "singularity", the solutions from both patches are shown to
have finite limits and are merged continuously as suggested by the work of
Hosomichi and Ribault. From this two point function, we can derive
b^{-2}/2-shift equations for AdS_2 D-branes. We show that discrete as well as
continuous AdS_2 branes are consistent with our novel shift equations without
any new restrictions.Comment: version to appear in JHEP - 12 pages now; sign error with impact on
some parts of the interpretation fixed; material added to become more
self-contained; role of bulk-boundary OPE in section 4 more carefully
discussed; 3 references adde
Calculation of Four Point Correlation Function of Logarithmic Conformal Field Theory Using AdS/CFT Correspondence
We use the correspondence between scalar field theory on AdS and induced
conformal field theory on its boundary to calculate correlation functions of
logarithmic conformal field theory in arbitrary dimensions.Our calculations
utilize the newly proposed method of nilpotent weights.We derive expressions
for the four point function assuming a generic interaction termComment: 7 pages, no figure
Three-leg correlations in the two component spanning tree on the upper half-plane
We present a detailed asymptotic analysis of correlation functions for the
two component spanning tree on the two-dimensional lattice when one component
contains three paths connecting vicinities of two fixed lattice sites at large
distance apart. We extend the known result for correlations on the plane to
the case of the upper half-plane with closed and open boundary conditions. We
found asymptotics of correlations for distance from the boundary to one of
the fixed lattice sites for the cases and .Comment: 16 pages, 5 figure
Extended chiral algebras in the SU(2)_0 WZNW model
We investigate the W-algebras generated by the integer dimension chiral
primary operators of the SU(2)_0 WZNW model. These have a form almost identical
to that found in the c=-2 model but have, in addition, an extended Kac-Moody
structure. Moreover on Hamiltonian reduction these SU(2)_0 W-algebras exactly
reduce to those found in c=-2. We explicitly find the free field
representations for the chiral j=2 and j=3 operators which have respectively a
fermionic doublet and bosonic triplet nature. The correlation functions of
these operators accounts for the rational solutions of the
Knizhnik-Zamolodchikov equation that we find. We explicitly compute the full
algebra of the j=2 operators and find that the associativity of the algebra is
only guaranteed if certain null vectors decouple from the theory. We conjecture
that these algebras may produce a quasi-rational conformal field theory.Comment: 18 pages LATEX. Minor corrections. Full j=2 algebra adde
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
Extended multiplet structure in Logarithmic Conformal Field Theories
We use the process of quantum hamiltonian reduction of SU(2)_k, at rational
level k, to study explicitly the correlators of the h_{1,s} fields in the
c_{p,q} models. We find from direct calculation of the correlators that we have
the possibility of extra, chiral and non-chiral, multiplet structure in the
h_{1,s} operators beyond the `minimal' sector. At the level of the vacuum null
vector h_{1,2p-1}=(p-1)(q-1) we find that there can be two extra non-chiral
fermionic fields. The extra indicial structure present here permeates
throughout the entire theory. In particular we find we have a chiral triplet of
fields at h_{1,4p-1}=(2p-1)(2q-1). We conjecture that this triplet algebra may
produce a rational extended c_{p,q} model. We also find a doublet of fields at
h_{1,3p-1}=(\f{3p}{2}-1)(\f{3q}{2}-1). These are chiral fermionic operators if
p and q are not both odd and otherwise parafermionic.Comment: 24 pages LATEX. Minor corrections and extra reference
Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas
We study a set of chiral symmetries contained in degenerate operators beyond
the `minimal' sector of the c(p,q) models. For the operators
h_{(2j+2)q-1,1}=h_{1,(2j+2)p-1} at conformal weight [ (j+1)p-1 ][ (j+1)q -1 ],
for every 2j \in N, we find 2j+1 chiral operators which have quantum numbers of
a spin j representation of SU(2). We give a free-field construction of these
operators which makes this structure explicit and allows their OPEs to be
calculated directly without any use of screening charges. The first non-trivial
chiral field in this series, at j=1/2, is a fermionic or para-fermionic
doublet. The three chiral bosonic fields, at j=1, generate a closed W-algebra
and we calculate the vacuum character of these triplet models.Comment: 23 pages Late
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