Connecting SLE and minisuperspace Liouville gravity

Understand

We show that Fokker-Planck equation for chordal SLE process under a simple rescaling of the probability density can be traced to the minisuperspace Wheeler-de Witt equation for boundary operator in 2d Liouville gravity.

• Insertion of an operator, calculating SLE critical exponent, corresponds to adding matter contribution to WdW equation.
• This observation may be useful for understanding of why SLE critical exponents are given by KPZ gravitational scaling dimensions.
• Possible applications of the obtained relation are discussed.