Spontaneous Lorentz symmetry breaking in nonlinear electrodynamics

We review some of the basic features and predictions of a gauge invariant spontaneous Lorentz symmetry breaking model arising from the nonzero vacuum expectation value of the electromagnetic tensor and leading to a nonlinear electrodynamics. The model is stable in the small Lorentz invariance violation approximation. The speed of light is independent of the frequency and one of the propagating modes is highly anisotropic. The bound (Delta c)/c < 10^{-32} is obtained for such anisotropy measured in perpendicular directions.Comment: 5 pages, no figures, Invited talk to the Fifth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 28-July 2, 201

The algebra of supertraces for 2+1 super de Sitter gravity

The algebra of the observables for 2+1 super de Sitter gravity, for one genus of the spatial surface is calculated. The algebra turns out to be an infinite Lie algebra subject to non-linear constraints. The constraints are solved explicitly in terms of five independent complex supertraces. These variables are the true degrees of freedom of the system and their quantized algebra generates a new structure which is referred to as a 'central extension' of the quantum algebra SU(2)q

Orthogonality Relations and Supercharacter Formulas of U(m|n) Representations

In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of complex conjugated and mixed representations. Our results are expressed in terms of the Young tableaux notation for irreducible representations. We use the supersymmetric Harish-Chandra-Itzykson-Zuber integral and the character expansion technique as mathematical tools for deriving these relations. As a byproduct we also obtain closed expressions for the supercharacters and dimensions of some particular irreducible U(m|n) representations. A new way of labeling the U(m|n) irreducible representations in terms of m + n numbers is proposed. Finally, as a corollary of our results, new identities among the dimensions of the irreducible representations of the unitary group U(N) are presented.Comment: 56 pages, LaTeX, changes only in the writing of the titl