Are Domain Walls in Spin Glasses Described by Stochastic Loewner Evolutions?

Domain walls for spin glasses are believed to be scale invariant invariant; a stronger symmetry, conformal invariance, has the potential to hold. The statistics of zero-temperature Ising spin glass domain walls in two dimensions are used to test the hypothesis that these domain walls are described by a Schramm-Loewner evolution SLE${}_{\kappa }$. Multiple tests are consistent with SLE${}_{\kappa }$, where $\kappa =2.30(5)$. Both conformal invariance and the domain Markov property are tested. The latter does not hold in small systems, but detailed numerical evidence suggests that it holds in the continuum limit.