Glass transition of hard spheres in high dimensions

We have investigated analytically and numerically the liquid-glass transition of hard spheres for dimensions d -> infinity in the framework of mode-coupling theory. The numerical results for the critical collective and self-nonergodicity parameters f(c)(k; d) and f(c)((s))(k; d) exhibit non-Gaussian k dependence even up to d = 800. f(c)((s))(k; d) and f(c)(k; d) differ for k similar to d(1/2), but become identical on a scale k similar to d, which is proven analytically. The critical packing fraction phi(c)(d) similar to d(2)2(-d) is above the corresponding Kauzmann packing fraction phi(K)(d) derived by a small cage expansion. Its quadratic pre-exponential factor is different from the linear one found earlier. The numerical values for the exponent parameter and therefore the critical exponents a and b depend on d, even for the largest values of d.