Representations Of Kac-Moody Algebras Research Articles

Kac-Moody and Virasoro characters from the perturbative Chern-Simons path integral

We evaluate to one loop the functional integral that computes the partition functions of Chern-Simons theories based on compact groups, using the background field method and a covariant gauge fixing. We compare our computation with the results of other, less direct methods. We find that our method correctly computes the characters of irreducible representations of Kac-Moody algebras. To extend the computation to non-compact groups we need to perform an appropriate analytic continuation of the partition function of the compact group. Non-vacuum characters are found by inserting a Wilson loop in the functional integral. We then extend our method to Euclidean Anti-de Sitter pure gravity in three dimensions. The explicit computation unveils several interesting features and lessons. The most important among them is that the very definition of gravity in the first-order Chern-Simons formalism requires non-trivial analytic continuations of the gauge fields outside their original domains of definition.

Vertex operator representations of Kac-Moody algebra

Abstract We construct various vertex operator representations of the Kac-Moody algebra in terms of free bosons. The realization of the algebra in terms of twisted bosons is briefly discussed.

NON-UNITARY SUPERSYMMETRIC CONFORMAL FIELD THEORIES AND SUPERSYMMETRIC SINE-GORDON EQUATION

We study coset construction of superconformal minimal models using admissible representations of Kac-Moody algebra. In particular, we study supersymmetric minimal models of Wn algebra, and in particular we argue that c = −5/2 cannot be considered as a minimal model of superconformal or super-W3 algebra. In the second part of the paper, we consider superconformal field theories whose perturbations correspond to breather-breather scattering in supersymmetric sine-Gordon equations, and find a family of theories with c = −3N(4N + 3)/2(N + 1), N = 1, 2, 3, …, which is the counterpart of the family of non-unitary theories with c = −2N(6N + 5)/(2N + 3), N = 1, 2, 3, …, among which N = 1 (c = −22/5) is the Yang-Lee edge singularity.

Vertex operators and Jordan fields

Abstract The construction of Lie algebras in terms of Jordan algebra generators is discussed. The key to the construction is the triality relation already incorporated into matrix products. A generalisation to Kac-Moody algebras in terms of vertex operators is proposed and may provide a clue for the construction of new representations of Kac-Moody algebras in terms of Jordan fields.

A construction of thec<1 modular invariant partition functions

Decomposition theorems for certain representations of Kac-Moody algebras which are needed for the construction of modular invariant unitary conformal models are proved. It is shown that allc<1 modular invariant models can then be recovered from gauged free fermionic models, including the exceptional cases.