Thursday, 1 August 2019

quantum field theory - Conformal compatification of Minkowski and AdS


How do I show that the compactification of Minkowski is given by the quadric uvηijxixj=0

with an overall scale equivalence in the coordinates.I get that for v0, the surface can be parametrized with the Minkowski coordinates. Now for v=0, I can have arbitrary values of u, which means basically two values, u=0 and u0. So are the infinities mapped to these points ? After that is it obvious that the conformal group acts on the space time defined by the quadric ?


From, uvηijxixj=1

if I have to show that the boundary of AdSd+1 is Minkowski in d dimensions, how do I take the limit ?




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