58 research outputs found
Vacuum Instability in Chern-Simons Theory, Null Vectors and Two-Dimensional Logarithmic Operators
A new relation between two-dimensional conformal field theories and
three-dimensional topologically massive gauge theories is found, where the
dynamical nature of the 3d theory is ultimately important.
It is shown that the those primary states in CFT which have non-unitary
descendants correspond in the 3d theory to supercritical charges and cause
vacuum instability. It is also shown that logarithmic operators separating the
unitary sector from a non-unitary one correspond to an exact zero energy ground
state in which case the 3d Hamiltonian naturally has a Jordan structure.Comment: 12 pages, Latex. 1 figur
A Rational Logarithmic Conformal Field Theory
We analyse the fusion of representations of the triplet algebra, the
maximally extended symmetry algebra of the Virasoro algebra at c=-2. It is
shown that there exists a finite number of representations which are closed
under fusion. These include all irreducible representations, but also some
reducible representations which appear as indecomposable components in fusion
products.Comment: 10 pages, LaTe
A Note on Four-Point Functions in Logarithmic Conformal Field Theory
The generic structure of 4-point functions of fields residing in
indecomposable representations of arbitrary rank is given. The presented
algorithm is illustrated with some non-trivial examples and permutation
symmetries are exploited to reduce the number of free structure-functions,
which cannot be fixed by global conformal invariance alone.Comment: Contribution to the Proceedings of the 37th International Symposium
Ahrenshoop on the Theory of Elementary Particles, 7p
Nonmeromorphic operator product expansion and C_2-cofiniteness for a family of W-algebras
We prove the existence and associativity of the nonmeromorphic operator
product expansion for an infinite family of vertex operator algebras, the
triplet W-algebras, using results from P(z)-tensor product theory. While doing
this, we also show that all these vertex operator algebras are C_2-cofinite.Comment: 21 pages, to appear in J. Phys. A: Math. Gen.; the exposition is
improved and one reference is adde
SU(2)_0 and OSp(2|2)_{-2} WZNW models : Two current algebras, one Logarithmic CFT
We show that the SU(2)_0 WZNW model has a hidden OSp(2|2)_{-2} symmetry. Both
these theories are known to have logarithms in their correlation functions. We
also show that, like OSp(2|2)_{-2}, the logarithmic structure present in the
SU(2)_0 model is due to the underlying c=-2 sector. We also demonstrate that
the quantum Hamiltonian reduction of SU(2)_0 leads very directly to the
correlation functions of the c=-2 model. We also discuss some of the novel
boundary effects which can take place in this model.Comment: 31 pages. Revised versio
From Percolation to Logarithmic Conformal Field Theory
The smallest deformation of the minimal model M(2,3) that can accommodate
Cardy's derivation of the percolation crossing probability is presented. It is
shown that this leads to a consistent logarithmic conformal field theory at
c=0. A simple recipe for computing the associated fusion rules is given. The
differences between this theory and the other recently proposed c=0 logarithmic
conformal field theories are underlined. The discussion also emphasises the
existence of invariant logarithmic couplings that generalise Gurarie's anomaly
number.Comment: 12 pages, 2 figures, minor changes mad
Modular transformation and boundary states in logarithmic conformal field theory
We study the model of logarithmic conformal field theory in the
presence of a boundary using symplectic fermions. We find boundary states with
consistent modular properties. A peculiar feature of this model is that the
vacuum representation corresponding to the identity operator is a
sub-representation of a ``reducible but indecomposable'' larger representation.
This leads to unusual properties, such as the failure of the Verlinde formula.
Despite such complexities in the structure of modules, our results suggest that
logarithmic conformal field theories admit bona fide boundary states.Comment: 7 pages, 1 table, revtex. Minor corrections, a comment adde
Notes on Generalised Nullvectors in logarithmic CFT
In these notes we discuss the procedure how to calculate nullvectors in
general indecomposable representations which are encountered in logarithmic
conformal field theories. In particular, we do not make use of any of the
restrictions which have been imposed in logarithmic nullvector calculations up
to now, especially the quasi-primarity of all Jordan cell fields.
For the quite well-studied c_{p,1} models we calculate examples of
logarithmic nullvectors which have not been accessible to the older methods and
recover the known representation structure. Furthermore, we calculate
logarithmic nullvectors in the up to now almost unexplored general augmented
c_{p,q} models and use these to find bounds on their possible representation
structures.Comment: 27 pages, 3 figures; v2: Corrected two typos, added one reference to
the conclusio
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