We discuss in this paper the conformal geometry of bi-invariant metrics on compact semisimple Lie groups. For this purpose we develop a conformal Cartan calculus adapted to this problem. In particular, we derive an explicit formula for the holonomy algebra of the normal conformal Cartan connection of a bi-invariant metric. As an example, we apply this calculus to the group SO(4). Its conformal ...

Pure spinor formalism and non-integrable exponential factors are used for constructing the conformal-invariant wave equation and Lagrangian density for massive fermion. It is proved that canonical Dirac Lagrangian for massive fermion is invariant under induced projective conformal transformations.

The general structure of the conformal anomaly and the dilaton’s effect to the anomaly are analysed. First we give a new formal proof of the statement that the conformal anomaly, in the theory which is conformal invariant at the classical level, is conformal invariant. The heat-kernel regularization and Fujikawa’s method are taken for the analysis. We present a new explicit result of the confor...

Abstract. We consider the GUT-like model with two scalar fields which has infinitesimal deviation from the conformal invariant fixed point at high energy region. In this case the dominating quantum effect is the conformal trace anomaly and the interaction between the anomaly-generated propagating conformal factor of the metric and the usual dimensional scalar field. This interaction leads to th...

The physical states in a world-volume model of a non-critical 3-brane are systematically constructed using techniques of four-dimensional conformal field theories on R × S 3 developed recently. Invariant combinations of creation modes under a special conformal transformation provide building blocks of physical states. Any state can be created by acting with such building blocks on a conformally...

The physical states in a world-volume model of a non-critical 3-brane are systematically constructed using techniques of four-dimensional conformal field theories on R × S 3 developed recently. Invariant combinations of creation modes under a special conformal transformation provide building blocks of physical states. Any state can be created by acting with such building blocks on a conformally...

Amputation of external legs is carried out explicitly for the conformal invariant three-point function involving two spinors and one vector field. Our results are consistent with the general result that amputing an external leg in a conformal invariant Green function replaces a field by its conformal partner in the Green function. A star-triangle relation involving two spinors and one vector fi...