UNIGE document Scientific Article
previous document  unige:10686  next document
add to browser collection
Title

SLE local martingales in logarithmic representations

Author
Published in Journal of Statistical Mechanics: Theory and Experiment. 2009, vol. 2009, no. 08, p. P08005
Abstract A space of local martingales of SLE-type growth processes forms a representation of Virasoro algebra, but apart from a few simplest cases, not much is known about this representation. The purpose of this paper is to exhibit examples of representations where L0 is not diagonalizable—a phenomenon characteristic of logarithmic conformal field theory. Furthermore, we observe that the local martingales bear a close relation to the fusion product of the boundary changing fields. Our examples reproduce first of all many familiar logarithmic representations at certain rational values of the central charge. In particular we discuss the case of SLEκ=6 describing the exploration path in critical percolation and its relation to the question of operator content of the appropriate conformal field theory of zero central charge. In this case one encounters logarithms in a probabilistically transparent way, through conditioning on a crossing event. But we also observe that some quite natural SLE variants exhibit logarithmic behavior at all values of κ, thus at all central charges and not only at specific rational values.
Keywords Stochastic loewner evolutionConformal field theory (theory)
Stable URL http://archive-ouverte.unige.ch/unige:10686
Full text
Article (Author postprint) (466 Kb) - public document Free access
Identifiers
Structures
139 hits and 53 downloads since 2010-08-10
Update
Export document
Format :
Citation style :