Physics – Mathematical Physics
Scientific paper
2003-05-30
AnnalesHenriPoincare5:289-326,2004
Physics
Mathematical Physics
41 pages, 4 figures
Scientific paper
10.1007/s00023-004-0170-z
We present an implementation in conformal field theory (CFT) of local finite conformal transformations fixing a point. We give explicit constructions when the fixed point is either the origin or the point at infinity. Both cases involve the exponentiation of a Borel subalgebra of the Virasoro algebra. We use this to build coherent state representations and to derive a close analog of Wick's theorem for the Virasoro algebra. This allows to compute the conformal partition function in non trivial geometries obtained by removal of hulls from the upper half plane. This is then applied to stochastic Loewner evolutions (SLE). We give a rigorous derivation of the equations, obtained previously by the authors, that connect the stochastic Loewner equation to the representation theory of the Virasoro algebra. We give a new proof that this construction enumerates all polynomial SLE martingales. When one of the hulls removed from the upper half plane is the SLE hull, we show that the partition function is a famous local martingale known to probabilists, thereby unravelling its CFT origin.
Bauer Michel
Bernard Denis
No associations
LandOfFree
Conformal transformations and the SLE partition function martingale does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Conformal transformations and the SLE partition function martingale, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Conformal transformations and the SLE partition function martingale will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-395639