Correlation functions for chiral primaries in D=6 Supergravity on AdS3×S3AdS_3 \times S^3

Six dimensional supergravities on $ADS_3 \times S^3$ present interest due to the role they play in the $AdS/CFT$ correspondence. The correspondence in this case states the equivalence between supergravity on the given background and a still unknown conformal field theory. The conformal field theory in question is expected to appear by deforming of the free conformal field theory on $S^N(T^4)$ in a way which preserves the superconformal symmetry. The purpose of this paper is to compute the first nontrivial corrections to the equations of motion for the chiral primary fields coming from supergravity. Using the methods already developed which involve nontrivial redefinitions of fields, we compute three-point correlation functions for scalar chiral primaries and notice similarities between their expressions and those obtained in the orbifold conformal field theory.Comment: 15 pages, harvmac bi

Filling a box with translates of two bricks

We give a new proof of the following interesting fact recently proved by Bower and Michael: if a d-dimensional rectangular box can be tiled using translates of two types of rectangular bricks, then it can also be tiled in the following way. We can cut the box across one of its sides into two boxes, one of which can be tiled with the first brick only and the other one with the second brick. Our proof relies on the Fourier Transform. We also show that no such result is true for three, or more, types of bricks

Fourier pairs of discrete support with little structure

We give a simple proof of the fact that there exist measures on the real line of discrete support, whose Fourier Transform is also a measure of discrete support, yet this Fourier pair cannot be constructed by repeatedly applying the Poisson Summation Formula finitely many times. More specifically the support of both the measure and its Fourier Tranform are not contained in a finite union of arithmetic progressions.Comment: The bibliography was missing from the previous versio