Joint ICTP/SISSA STAT_PHYS Seminar on 7 February 2012

[ivanisse]

JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINAR

Tuesday, 7 February 2012  -   11:30 a.m.

Luigi Stasi Seminar Room - Leonardo Bldg. - 1st floor


Ben Doyon (King's College, London)

" Conformal maps and conformal algebra "

Abstract:

 From standard textbooks we know that derivatives of functions on a 
group manifold generate the associated Lie algebra. One can generalize 
the concept of Lie algebra to a very natural concept called conformal 
algebra, in the same spirit as that by which one goes from real to 
complex numbers. I'll consider a certain infinite-dimensional manifold 
whose points are conformal maps, and derivatives of functions on this 
manifold (i.e. functionals of conformal maps). I'll show that not only 
they give rise to the Witt or Virasoro algebra, but, when looking at 
covariant derivatives, they give rise to the simplest conformal algebra 
(the Virasoro vertex operator algebra). This allows one to re-interpret 
aspects of conformal field theory, like partition function and 
stress-energy tensor, through covariant conformal derivatives, and to 
define such objects in other contexts, like random loop models. In this 
talk I'll try to introduce all necessary concepts just from basic notions.