16 research outputs found
The Adapted Ordering Method for Lie Algebras and Superalgebras and their Generalizations
In 1998 the Adapted Ordering Method was developed for the representation
theory of the superconformal algebras in two dimensions. It allows: to
determine maximal dimensions for a given type of space of singular vectors, to
identify all singular vectors by only a few coefficients, to spot subsingular
vectors and to set the basis for constructing embedding diagrams. In this
article we present the Adapted Ordering Method for general Lie algebras and
superalgebras, and their generalizations, provided they can be triangulated. We
also review briefly the results obtained for the Virasoro algebra and for the
N=2 and Ramond N=1 superconformal algebras.Comment: Many improvements in the redaction for pedagogical purposes. Latex,
11 page
Superconformal Primary Fields on a Graded Riemann Sphere
Primary superfields for a two dimensional Euclidean superconformal field
theory are constructed as sections of a sheaf over a graded Riemann sphere. The
construction is then applied to the N=3 Neveu-Schwarz case. Various quantities
in the N=3 theory are calculated and discussed, such as formal elements of the
super-Mobius group, and the two-point function.Comment: LaTeX2e, 23 pages; fixed typos, sorted references, modified
definition of primary superfield on page
Analytic Expressions for Singular Vectors of the Superconformal Algebra
Using explicit expressions for a class of singular vectors of the
(untwisted) algebra and following the approach of Malikov-Feigin-Fuchs and
Kent, we show that the analytically extended Verma modules contain two linearly
independent neutral singular vectors at the same grade. We construct this two
dimensional space and we identify the singular vectors of the original Verma
modules. We show that in some Verma modules these expressions lead to two
linearly independent singular vectors which are at the same grade and have the
same charge.Comment: 35 pages, LATE
Stochastic evolutions in superspace and superconformal field theory
Some stochastic evolutions of conformal maps can be described by SLE and may
be linked to conformal field theory via stochastic differential equations and
singular vectors in highest-weight modules of the Virasoro algebra. Here we
discuss how this may be extended to superconformal maps of N=1 superspace with
links to superconformal field theory and singular vectors of the N=1
superconformal algebra in the Neveu-Schwarz sector.Comment: 13 pages, LaTe
N=2 Supersymmetry and Bailey Pairs
We demonstrate that the Bailey pair formulation of Rogers-Ramanujan
identities unifies the calculations of the characters of and
supersymmetric conformal field theories with the counterpart theory with no
supersymmetry. We illustrate this construction for the (Ising) model
where the Bailey pairs have been given by Slater. We then present the general
unitary case. We demonstrate that the model is derived from
by a Bailey renormalization flow and conclude by obtaining the
model and the unitary model with central charge Comment: 32 pages in harvmac, no figure
Manifestly Supersymmetric RG Flows
Renormalisation group (RG) equations in two-dimensional N=1 supersymmetric
field theories with boundary are studied. It is explained how a manifestly N=1
supersymmetric scheme can be chosen, and within this scheme the RG equations
are determined to next-to-leading order. We also use these results to revisit
the question of how brane obstructions and lines of marginal stability appear
from a world-sheet perspective.Comment: 22 pages; references added, minor change
D-branes and SQCD in Non-Critical Superstring Theory
Using exact boundary conformal field theory methods we analyze the D-brane
physics of a specific four-dimensional non-critical superstring theory which
involves the N=2 SL(2)/U(1) Kazama-Suzuki model at level 1. Via the holographic
duality of hep-th/9907178 our results are relevant for D-brane dynamics in the
background of NS5-branes and D-brane dynamics near a conifold singularity. We
pay special attention to a configuration of D3- and D5-branes that realizes N=1
supersymmetric QCD and discuss the massless spectrum and classical moduli of
this setup in detail. We also comment briefly on the implications of this
construction for the recently proposed generalization of the AdS/CFT
correspondence by Klebanov and Maldacena within the setting of non-critical
superstrings.Comment: harvmac, 47 pages, 6 figures; v4 same as v3 due to submission erro
Unitarity of rational N=2 superconformal theories
We demonstrate that all rational models of the N=2 super Virasoro algebra are
unitary. Our arguments are based on three different methods: we determine Zhu's
algebra (for which we give a physically motivated derivation) explicitly for
certain theories, we analyse the modular properties of some of the vacuum
characters, and we use the coset realisation of the algebra in terms of su_2
and two free fermions.
Some of our arguments generalise to the Kazama-Suzuki models indicating that
all rational N=2 supersymmetric models might be unitary.Comment: LaTeX (+amssym.def), 28 pages; minor changes in content, some
references added, final versio
On the complete classification of the unitary N=2 minimal superconformal field theories
Aiming at a complete classification of unitary N=2 minimal models (where the
assumption of space-time supersymmetry has been dropped), it is shown that each
modular invariant candidate of a partition function for such a theory is indeed
the partition function of a minimal model. A family of models constructed via
orbifoldings of either the diagonal model or of the space-time supersymmetric
exceptional models demonstrates that there exists a unitary N=2 minimal model
for every one of the allowed partition functions in the list obtained from
Gannon's work.
Kreuzer and Schellekens' conjecture that all simple current invariants can be
obtained as orbifolds of the diagonal model, even when the extra assumption of
higher-genus modular invariance is dropped, is confirmed in the case of the
unitary N=2 minimal models by simple counting arguments.Comment: 53 pages; Latex; minor changes in v2: intro expanded, references
added, typos corrected, footnote added on p31; renumbering of sections; main
theorem reformulated for clarity, but contents unchanged. Minor revisions in
v3: typos corrected, footnotes 5, 6 added, lemma 1 and section 3.3.2
rewritten for greater generality, section 3.3 review removed. To appear in
Comm. Math. Phy