3,406 research outputs found
Flat Connections for Characters in Irrational Conformal Field Theory
Following the paradigm on the sphere, we begin the study of irrational
conformal field theory (ICFT) on the torus. In particular, we find that the
affine-Virasoro characters of ICFT satisfy heat-like differential equations
with flat connections. As a first example, we solve the system for the general
coset construction, obtaining an integral representation for the general
coset characters. In a second application, we solve for the high-level
characters of the general ICFT on simple , noting a simplification for the
subspace of theories which possess a non-trivial symmetry group. Finally, we
give a geometric formulation of the system in which the flat connections are
generalized Laplacians on the centrally-extended loop group.Comment: harvmac (answer b to question) 40 pages. LBL-35718, UCB-PTH-94/1
Two Large Examples in Orbifold Theory: Abelian Orbifolds and the Charge Conjugation Orbifold on su(n)
Recently the operator algebra and twisted vertex operator equations were
given for each sector of all WZW orbifolds, and a set of twisted KZ equations
for the WZW permutation orbifolds were worked out as a large example. In this
companion paper we report two further large examples of this development. In
the first example we solve the twisted vertex operator equations in an abelian
limit to obtain the twisted vertex operators and correlators of a large class
of abelian orbifolds. In the second example, the twisted vertex operator
equations are applied to obtain a set of twisted KZ equations for the
(outer-automorphic) charge conjugation orbifold on su(n \geq 3).Comment: 58 pages, v2: three minor typo
Ward Identities for Affine-Virasoro Correlators
Generalizing the Knizhnik-Zamolodchikov equations, we derive a hierarchy of
non-linear Ward identities for affine-Virasoro correlators. The hierarchy
follows from null states of the Knizhnik-Zamolodchikov type and the assumption
of factorization, whose consistency we verify at an abstract level. Solution of
the equations requires concrete factorization ans\"atze, which may vary over
affine-Virasoro space. As a first example, we solve the non-linear equations
for the coset constructions, using a matrix factorization. The resulting coset
correlators satisfy first-order linear partial differential equations whose
solutions are the coset blocks defined by Douglas.Comment: 53 pages, Latex, LBL-32619, UCB-PTH-92/24, BONN-HE-92/2
Flat Connections and Non-Local Conserved Quantities in Irrational Conformal Field Theory
Irrational conformal field theory (ICFT) includes rational conformal field
theory as a small subspace, and the affine-Virasoro Ward identities describe
the biconformal correlators of ICFT. We reformulate the Ward identities as an
equivalent linear partial differential system with flat connections and new
non-local conserved quantities. As examples of the formulation, we solve the
system of flat connections for the coset correlators, the correlators of the
affine-Sugawara nests and the high-level -point correlators of ICFT.Comment: 40 pages, Latex, UCB-PTH-93/33, LBL-34901, CPTH-A277.129
Solving the Ward Identities of Irrational Conformal Field Theory
The affine-Virasoro Ward identities are a system of non-linear differential
equations which describe the correlators of all affine-Virasoro constructions,
including rational and irrational conformal field theory. We study the Ward
identities in some detail, with several central results. First, we solve for
the correlators of the affine-Sugawara nests, which are associated to the
nested subgroups . We also find an
equivalent algebraic formulation which allows us to find global solutions
across the set of all affine-Virasoro constructions. A particular global
solution is discussed which gives the correct nest correlators, exhibits
braiding for all affine-Virasoro correlators, and shows good physical behavior,
at least for four-point correlators at high level on simple . In rational
and irrational conformal field theory, the high-level fusion rules of the
broken affine modules follow the Clebsch-Gordan coefficients of the
representations.Comment: 45 pages, Latex, UCB-PTH-93/18, LBL-34111, BONN-HE-93/17. We
factorize the biconformal nest correlators of the first version, obtaining
the conformal correlators of the affine-Sugawara nests on g/h_1/.../h_
Semi-Classical Blocks and Correlators in Rational and Irrational Conformal Field Theory
The generalized Knizhnik-Zamolodchikov equations of irrational conformal
field theory provide a uniform description of rational and irrational conformal
field theory. Starting from the known high-level solution of these equations,
we first construct the high-level conformal blocks and correlators of all the
affine-Sugawara and coset constructions on simple g. Using intuition gained
from these cases, we then identify a simple class of irrational processes whose
high-level blocks and correlators we are also able to construct.Comment: 53 pages, Latex. Revised version with extended discussion of phases
and secondarie
The Lie h-Invariant Conformal Field Theories and the Lie h-Invariant Graphs
We use the Virasoro master equation to study the space of Lie h-invariant
conformal field theories, which includes the standard rational conformal field
theories as a small subspace. In a detailed example, we apply the general
theory to characterize and study the Lie h-invariant graphs, which classify the
Lie h-invariant conformal field theories of the diagonal ansatz on SO(n). The
Lie characterization of these graphs is another aspect of the recently observed
Lie group-theoretic structure of graph theory.Comment: 38p
Systematic approach to cyclic orbifolds
We introduce an orbifold induction procedure which provides a systematic
construction of cyclic orbifolds, including their twisted sectors. The
procedure gives counterparts in the orbifold theory of all the
current-algebraic constructions of conformal field theory and enables us to
find the orbifold characters and their modular transformation properties.Comment: 39 pages, LaTeX. v2,3: references added. v4: typos correcte
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