Cartan Generators Research Articles

Induced hypermultiplet self-interactions in N = 2 gauge theories

We calculate the charged hypermultiplet low-energy effective action in the Coulomb branch of the 4D, N = 2 gauge theory, by using the harmonic superspace approach. We find that the unique leading contribution is given by the harmonic-analytic Lagrangian of the fourth order in the hypermultiplet superfields, with the induced coupling constant being proportional to central charges of N = 2 SUSY algebra. The central charges are identified with Cartan generators of the internal symmetry, and they give BPS masses to the hypermultiplets. The induced hyper-Ka¨hler metrics appear to be the Taub-NUT metric or its higher-dimensional generalizations. Simultaneously, non-trivial scalar potentials are produced. Within the harmonic superspace method, we show an equivalence between the two known approaches to the 4D central charges. In the first one, the central charges are obtained via the Scherk-Schwarz dimensional reduction from six dimensions, whereas in the second one they are generated by a covariantly constant background gauge superfield. Our analysis is extended to a more general situation with non-vanishing Fayet-Iliopoulos (FI) terms. The perturbatively induced Taub-NUT self-coupling in the Coulomb branch is found to be stable against adding the FI term, whereas the non-perturbatively generated (Eguchi-Hanson-type) hypermultiplet self-interaction is proposed for the Higgs branch.

Polynomial relations in the centre ofU q (sl(N))

When the parameter of deformation q is a m-th root of unity, the centre of U_q(sl(N))$ contains, besides the usual q-deformed Casimirs, a set of new generators, which are basically the m-th powers of all the Cartan generators of U_q(sl(N)). All these central elements are however not independent. In this letter, generalising the well-known case of U_q(sl(2)), we explicitly write polynomial relations satisfied by the generators of the centre. Application to the parametrization of irreducible representations and to fusion rules are sketched.