The slicing conjecture for isotropic constants

For a convex body $K\subseteq\mathbb{R}^d$, let $L_K$ denote its isotropic constant. The slicing conjecture. There exists a universal constant $c_3>0$ such that for every dimension $d$ and every convex body $K\subseteq\mathbb{R}^d$,

$$L_K\leq c_3.$$

The paper states that this universal boundedness of isotropic constants is equivalent to the hyperplane-section formulation of the slicing conjecture, and discusses its equivalence with Meckes's weak conjecture and Vempala's question. The conjecture remains open in the source.