Abstract:
Scharmm–Loewner evolution (SLE) and conformal field theory (CFT)
are popular and widely used instruments to study critical behavior of
two-dimensional models, but they use different objects. While SLE has
natural connection with lattice models and is suitable for strict proofs, it
lacks computational and predictive power of conformal field theory. To
provide a way for the concurrent use of SLE and CFT we consider CFT
correlation functions which are martingales with respect to SLE. We
establish connection between parameters of Schramm–Loewner evolution on
coset space and algebraic data of coset conformal field theory. Then we
check the consistency of our approach with the behaviour of parafermionic
and minimal models. Coset models are connected with off-critical massive
field theories and we discuss implications for SLE.
Fulltext:
PDF file (181 kB)