Friday, June 18, 2010 ... //

Weinberg on 6D methods in AdS5/CFT4

After many years of active work in cosmology, Steven Weinberg decided to dedicate some of his time and energy to string-theory-inspired problems for a while:

Six-dimensional Methods for Four-dimensional Conformal Field Theories
The AdS5 space is a hyperboloid in a 4+2-dimensional space: "X^2" is (plus minus) "R^2". Instead, Weinberg describes it as a projective space - with the identification of vectors that differ by scaling.

In this 5D space - which is still an AdS5 parameterized in a different way - he defines the hypercone by the condition "X_{6}.X_{6}=0". And he projects the fields from the bigger space to the hypercone and derives some power laws for the scaling of the CFT fields in a new way - which are different for spinors and for other, ordinary tensors.

At this level, it is a kinematic trick - one that makes the conformal symmetry (and not just the Lorentz symmetry and the spherical inversion) more manifest - and no nontrivial dynamical facts about the supergravity or the gauge theory are derived, as far as I can say. However, it's still cool to see Weinberg thinking about the newer developments of what remains his #1 grateful discipline.