On Certain Two Dimensional Integrals that Appear In Conformal Field Theory
نویسنده
چکیده
In the framework of perturbative QCD at large Q and low x, the conformal (global) group of transformations in the transverse coordinate space plays a crucial role. Indeed Lipatov and his collaborators [1] have derived the master equation for the derivative of the gluon structure function with respect to x by resuming the leading ( αs ( Q̄ ) log(1/x) )n terms at fixed αs ( Q̄ ) . This derivative is a convolution in the transverse space of the gluon structure function times a conformal invariant kernel (BKKL kernel). All the relevant observables are then expressed as an expansion over the basis E of the conformal eigenfunctions of this kernel. The integer n is the conformal spin and iν corresponds to a continuous imaginary scaling dimension. Among others, the elastic off mass shell gluon-gluon amplitude corresponding to the exchange of the bare QCD hard Pomeron [1, 2] and the conformal invariant triple
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