37 research outputs found
Logarithmic intertwining operators and W(2,2p-1)-algebras
For every , we obtained an explicit construction of a family of
-modules, which decompose as direct sum of simple Virasoro
algebra modules. Furthermore, we classified all irreducible self-dual
-modules, we described their internal structure, and
computed their graded dimensions. In addition, we constructed certain hidden
logarithmic intertwining operators among two ordinary and one logarithmic
-modules. This work, in particular, gives a mathematically
precise formulation and interpretation of what physicists have been referring
to as "logarithmic conformal field theory" of central charge
. Our explicit construction can be
easily applied for computations of correlation functions. Techniques from this
paper can be used to study the triplet vertex operator algebra
and other logarithmic models.Comment: 22 pages; v2: misprints corrected, other minor changes. Final version
to appear in Journal of Math. Phy
An explicit realization of logarithmic modules for the vertex operator algebra W_{p,p'}
By extending the methods used in our earlier work, in this paper, we present
an explicit realization of logarithmic \mathcal{W}_{p,p'}-modules that have
L(0) nilpotent rank three. This was achieved by combining the techniques
developed in \cite{AdM-2009} with the theory of local systems of vertex
operators \cite{LL}. In addition, we also construct a new type of extension of
, denoted by . Our results confirm several
claims in the physics literature regarding the structure of projective covers
of certain irreducible representations in the principal block. This approach
can be applied to other models defined via a pair screenings.Comment: 18 pages, v2: one reference added, other minor change
Logarithmic vertex algebras related to sp(4)
We present several results and conjectures pertaining to parafermion vertex algebra and related logarithmic vertex algebras. Starting from the tensor product of two copies of the singlet vertex algebra M(2), we consider various subalgebras that appear in its decomposition including N-1(sl(2)) and its Z2-fixed point algebra, and the S2-symmetric orbifold of the singlet vertex algebra M(2). In particular, we show that N-1(sl(2)) has an extension to a W-algebra of type (2, 3, 4, 5, 6, 7, 8). Finally we state some conjectures about singlet and triplet type W-algebras of type sp(4) and their characters
On coset vertex algebras with central charge 1
We present a coset realization of the vertex operator algebra with central charge .
We investigate the vertex operator algebra (resp. ) as a vertex
subalgebra of (resp. ). Our construction is based on the
boson-fermion correspondence and certain conformal embeddings
Representations of certain non-rational vertex operator algebras of affine type
In this paper we study a series of vertex operator algebras of integer level
associated to the affine Lie algebra . These vertex operator
algebras are constructed by using the explicit construction of certain singular
vectors in the universal affine vertex operator algebra at the
integer level. In the case or , we explicitly determine Zhu's
algebras and classify all irreducible modules in the category . In
the case , we show that the vertex operator algebra contains
two linearly independent singular vectors of the same conformal weight.Comment: 15 pages, LaTeX; final version, to appear in J. Algebr
Conformal embeddings in affine vertex superalgebras
This paper is a natural continuation of our previous work on conformal
embeddings of vertex algebras [6], [7], [8]. Here we consider conformal
embeddings in simple affine vertex superalgebra where
is a basic
classical simple Lie superalgebras. Let
be the subalgebra of generated by . We
first classify all levels for which the embedding in is conformal. Next we prove that, for a
large family of such conformal levels, is a completely
reducible --module and obtain
decomposition rules. Proofs are based on fusion rules arguments and on the
representation theory of certain affine vertex algebras. The most interesting
case is the decomposition of as a finite, non
simple current extension of . This
decomposition uses our previous work [10] on the representation theory of
.Comment: Latex file, 45 pages, to appear in Advances in Mathematic
Fusion rules and complete reducibility of certain modules for affine Lie algebras
We develop a new method for obtaining branching rules for affine Kac-Moody
Lie algebras at negative integer levels. This method uses fusion rules for
vertex operator algebras of affine type. We prove that an infinite family of
ordinary modules for affine vertex algebra of type A investigated in Adamovi\'c
and O. Per\v{s}e (2008) is closed under fusion. Then we apply these fusion
rules on explicit bosonic realization of level -1 modules for the affine Lie
algebra of type , obtain a new proof of complete reducibility
for these representations, and the corresponding decomposition for . We also obtain the complete reducibility of the associated level -1 modules
for affine Lie algebra of type . Next we notice that the
category of modules at level obtained in
Per\v{s}e (2012) has the isomorphic fusion algebra. This enables us to
decompose certain and --modules at negative levels.Comment: 18 pages; final version, to appear in Journal of Algebra and Its
Application
Defining relations for minimal unitary quantum affine W-algebras
We prove that any unitary highest weight module over a universal minimal
quantum affine -algebra at non-critical level descends to its simple
quotient. We find the defining relations of the unitary simple minimal quantum
affine -algebras and the list of all their irreducible positive energy
modules. We also classify all irreducible highest weight modules for the simple
affine vertex algebras in the cases when the associated simple minimal
-algebra is unitary.Comment: Latex file, 24 pages, revised versio
Lie superalgebras and irreducibility of A_1^(1)-modules at the critical level
We introduce the infinite-dimensional Lie superalgebra and
construct a family of mappings from certain category of -modules
to the category of A_1^(1)-modules of critical level. Using this approach, we
prove the irreducibility of a family of A_1^(1)-modules at the critical level.
As a consequence, we present a new proof of irreducibility of certain
Wakimoto modules. We also give a natural realizations of irreducible quotients
of relaxed Verma modules and calculate characters of these representations.Comment: 21 pages, Late
The N=1 triplet vertex operator superalgebras
We introduce a new family of C_2-cofinite N=1 vertex operator superalgebras
SW(m), , which are natural super analogs of the triplet vertex
algebra family W(p), , important in logarithmic conformal field
theory. We classify irreducible SW(m)-modules and discuss logarithmic modules.
We also compute bosonic and fermionic formulas of irreducible SW(m) characters.
Finally, we contemplate possible connections between the category of
SW(m)-modules and the category of modules for the quantum group
U^{small}_q(sl_2), q=e^{\frac{2 \pi i}{2m+1}}, by focusing primarily on
properties of characters and the Zhu's algebra A(SW(m)). This paper is a
continuation of arXiv:0707.1857.Comment: 53 pages; v2: references added; v3: a few changes; v4: final version,
to appear in CM