We consider the non-interacting massive Wess-Zumino model in four-dimensional anti-de Sitter space and show that the conformal dimensions of the corresponding boundary fields satisfy the relations expected from superconformal invariance. In some cases the irregular mode must be used for one of the scalar fields.

Using the Wilson renormalization group, we show that if no integrated vector operator of scaling dimension -1 exists, then scale invariance implies conformal invariance. By using the Lebowitz inequalities, we prove that this necessary condition is fulfilled in all dimensions for the Ising universality class. This shows, in particular, that scale invariance implies conformal invariance for the t...

We show that in a two-dimensional σ-model whose fields only depend on one target space coordinate , the O(d, d) invariance of the conformal invariance conditions observed at one loop is preserved at two loops (in the general case with torsion) and at three loops (in the case without torsion). Duality invariance has proved to be an immensely fruitful concept in string theory. A particular aspect...

Supersymmetry and Lorentz invariance are closely related as both are spacetime symmetries. Terms can be added to Lagrangians that explicitly break either supersymmetry or Lorentz invariance. It is possible to include terms which violate Lorentz invariance but maintain invariance under supersymmetric transformations. I illustrate this with some simple extensions of the original Wess-Zumino model.

One of the most frequently used procedures for measurement invariance testing is the multigroup confirmatory factor analysis (MGCFA). Muthén and Asparouhov recently proposed a new approach to test for approximate rather than exact measurement invariance using Bayesian MGCFA. Approximate measurement invariance permits small differences between parameters otherwise constrained to be equal in the ...

In this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by Jones [12] for length-biased data.The approach is based on the invariance principle for the empirical processes proved by Horváth [10]. All simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by ...