65 research outputs found
On The Characters of Parafermionic Field Theories
We study cosets of the type , where is any Lie algebra at
level and rank . These theories are parafermionic and their characters
are related to the string functions, which are generating functions for the
multiplicities of weights in the affine representations. An identity for the
characters is described, which apply to all the algebras and all the levels.
The expression is of the Rogers Ramanujan type. We verify this conjecture, for
many algebras and levels, using Freudenthal Kac formula, which calculates the
multiplicities in the affine representations, recursively, up to some grade.
Our conjecture encapsulates all the known results about these string functions,
along with giving a vast wealth of new ones.Comment: 13 pages. The fortran program ALGEBRA.for is available from the
source file
Galois groups in rational conformal field theory II. The discriminant
We express the discriminant of the polynomial relations of the fusion ring,
in any conformal field theory, as the product of the rows of the modular matrix
to the power -2. The discriminant is shown to be an integer, always, which is a
product of primes which divide the level. Detailed formulas for the
discriminant are given for all WZW conformal field theories.Comment: 19 pages, one table. Minor typos correcte
On New Conformal Field Theories with Affine Fusion Rules
Some time ago, conformal data with affine fusion rules were found. Our
purpose here is to realize some of these conformal data, using systems of free
bosons and parafermions. The so constructed theories have an extended
algebras which are close analogues of affine algebras. Exact character formulae
is given, and the realizations are shown to be full fledged unitary conformal
field theories.Comment: Minor correction in an example and some typo
The string functions as -diagrams
We discuss our conjecture for simply laced Lie algebras level two string
functions of mark one fundamental weights and prove it for the
algebra. To prove our conjecture we introduce -diagrams and examine the
diagrammatic interpretations of known identities by Euler, Cauchy, Heine,
Jacobi and Ramanujan. Interestingly, the diagrammatic approach implies these
identities are related in the sense that they represent the first few terms in
an infinite series of diagrammatic identities. Furthermore, these diagrammatic
identities entail all the identities needed to prove our conjecture as well as
generalise it to all level two string functions. As such, our main
objective is proving these series of diagrammatic identities thus extending the
works mentioned and establishing our conjecture for the level two
string functions.Comment: 39 page
New String Theories And Their Generation Number
New heterotic string theories in four dimensions are constructed by tensoring
a nonstandard SCFT along with some minimal SCFT's. All such theories are
identified and their particle generation number is found. We prove that from
the infinite number of new heterotic string theories only the {6} theory
predicts three generations as seen in nature which makes it an interesting
candidate for further study.Comment: 18 pages, 1 table and no figure
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