Busemann–Petty centroid inequality formulation of the slicing conjecture

Let $G\subset\mathbb{R}^d$ be a convex symmetric body in isotropic position, and let $L(G)$ denote its isotropic constant. Slicing conjecture. There is a constant $C>0$ independent of $d\in\mathbb{N}$ such that

$$L(G)\le C$$

for every convex symmetric body $G\subset\mathbb{R}^d$ in isotropic position. The best general bound currently available is $L(G)=O(d^{1/4})$, so the conjectured dimension-independent bound remains open and has several equivalent formulations.