The embedding structure of unitary N=2 minimal models

We derive the embedding structure of unitary N=2 minimal models and show as a result that these representations have a degeneration of uncharged singular states. This corrects some earlier mistakes made in the literature. We discuss the connexion to the N=2 character formulae and finally give a proof for the embedding diagrams.Comment: Latex, 16 page

Transmutations between Singular and Subsingular Vectors of the N=2 Superconformal Algebras

We present subsingular vectors of the N=2 superconformal algebras other than the ones which become singular in chiral Verma modules, reported recently by Gato-Rivera and Rosado. We show that two large classes of singular vectors of the Topological algebra become subsingular vectors of the Antiperiodic NS algebra under the topological untwistings. These classes consist of BRST- invariant singular vectors with relative charges $q=-2,-1$ and zero conformal weight, and no-label singular vectors with $q=0,-1$. In turn the resulting NS subsingular vectors are transformed by the spectral flows into subsingular and singular vectors of the Periodic R algebra. We write down these singular and subsingular vectors starting from the topological singular vectors at levels 1 and 2.Comment: 21 pages, Latex. Minor improvements. Very similar to the version published in Nucl. Phys.

Analytic Expressions for Singular Vectors of the N=2N=2 Superconformal Algebra

Using explicit expressions for a class of singular vectors of the $N=2$ (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

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

An Introduction to Conformal Field Theory

A comprehensive introduction to two-dimensional conformal field theory is given.Comment: 69 pages, LaTeX; references adde

Singular dimensions of the N = 2 superconformal algebras. I

Verma modules of superconfomal algebras can have singular vector spaces with dimensions greater than 1. Following a method developed for the Virasoro algebra by Kent, we introduce the concept of adapted orderings on superconformal algebras. We prove several general results on the ordering kernels associated to the adapted orderings and show that the size of an ordering kernel implies an upper limit for the dimension of a singular vector space. We apply this method to the topological N = 2 algebra and obtain the maximal dimensions of the singular vector spaces in the topological Verma modules: 0, 1, 2 or 3 depending on the type of Verma module and the type of singular vector. As a consequence we prove the conjecture of Gato-Rivera and Rosado on the possible existing types of topological singular vectors (4 in chiral Verma modules and 29 in complete Verma modules). Interestingly, we have found two-dimensional spaces of singular vectors at level 1. Finally, by using the topological twists and the spectral flows, we also obtain the maximal dimensions of the singular vector spaces for the Neveu-Schwarz N = 2 algebra (0, 1 or 2) and for the Ramond N = 2 algebra (0, 1, 2 or 3).M.D. is supported by a DAAD fellowship and in part by NSF grant PHY-98-02709.info:eu-repo/grantAgreement/EC/FP7/Peer Reviewe