Thin $\mathrm{II}_{1}$ factors with no Cartan subalgebras

It is a wide open problem to give an intrinsic criterion for a II1 factor M to admit a Cartan subalgebra A. When A⊂M is a Cartan subalgebra, the A-bimodule L2(M) is simple in the sense that the left and right actions of A generate a maximal abelian subalgebra of B(L2(M)). A II1 factor M that admits such a subalgebra A is said to be s-thin. Very recently, Popa discovered an intrinsic local criterion for a II1 factor M to be s-thin and left open the question whether all s-thin II1 factors admit a Cartan subalgebra. We answer this question negatively by constructing s-thin II1 factors without Cartan subalgebras.