A world-volume model of non-critical 3-brane is quantized in a strong coupling phase where fluctuations of the conformal mode become dominant. This phase, called the conformal-mode dominant phase, is realized at the very high energy far beyond the Planck mass scale. We separately treat the conformal mode and the traceless mode and quantize the conformal mode non-perturbatively, while the tracel...

This paper develops the basic theory of conformal structures on finite subdivision rules. The work depends heavily on the use of expansion complexes, which are defined and discussed in detail. It is proved that a finite subdivision rule with bounded valence and mesh approaching 0 is conformal (in the combinatorial sense) if there is a partial conformal structure on the model subdivision complex...

The conformal algebra of a 1+3 decomposable spacetime can be computed from the Conformal Killing Vectors (CKV) of the 3-space. It is shown that the general form of such a 3-CKV is the sum of a gradient CKV and a Killing or homothetic 3vector. It is proved that spaces of constant curvature always admit such conformal Killing vectors. As an example the complete conformal algebra of a Gödel type s...

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...

A novel robust adaptive beamforming method for conformal array is proposed. By using interpolation technique, the cylindrical conformal array with directional antenna elements is transformed to a virtual uniform linear array with omni-directional elements. This method can compensate the amplitude and mutual coupling errors as well as desired signal point errors of the conformal array efficientl...

Conformal blocks form a system of vector bundles over the moduli space of complex curves with marked points. We discuss various aspects of these bundles. In particular, we present conjectures about the dimensions of sub-bundles. They imply a Verlinde formula for non-simply connected groups like PGL(n, C). We then explain how conformal blocks enter in the construction of conformal field theories...

The well known conformal covariance of the Dirac operator acting on spinor fields does not extend to its powers in general. For odd powers of the Dirac operator we derive an algorithmic construction in terms of associated tractor bundles computing correction terms in order to achieve conformal covariance. These operators turn out to be formally (anti-) self-adjoint. Working out this algorithm w...

We discuss non-relativistic conformal algebras generalizing the Schrödinger algebra. One instance of these algebras is a conformal, acceleration-extended, Galilei algebra, which arises also as a contraction of the relativistic conformal algebra. In two dimensions, this admits an “exotic” central extension, whereby boosts do not commute. We study general properties of non-relativistic conformal ...

We calculate conformal anomalies in noncommutative gauge theories by using path integral method (Fujikawa’s method). As well as the axial anomalies and chiral gauge anomalies, the conformal anomalies take the form of the straightforward Moyal deformation in the corresponding conformal anomalies in ordinary gauge theories. However, Moyal star product leads the difference in the coefficient of th...

BGG-operators form sequences of invariant differential operators and the first of these is overdetermined. Interesting equations in conformal geometry described by these operators are those for Einstein scales, conformal Killing forms and conformal Killing tensors. We present a deformation procedure of the tractor connection which yields an invariant prolongation of the first operator. The expl...