Abstract:
It has been conjectured in 1971 by Polyakov that critical phenomena
have conformal invariance, both in two and three dimensions. While the
two dimensional case has been intensely studied, the role of conformal
invariance in d=3 is not fully clarified. We will describe which parts
of conformal field theory carry over from d=2 to d=3. We will describe
the `conformal bootstrap' equations, whose solutions should give
conformally invariant algebras of local operators in d=3. The simplest
case is the operator algebra corresponding to the critical point of
the 3d Ising model. We conjecture that this operator algebra can be
characterized by a minimal central charge condition. Numerical
evidence for this conjecture will be presented. (based on
arxiv:1403.4545).