Natalie M. Paquette, Daniel Persson, and Roberto Volpato (Stanford, Sweden, Italy) published a mathematically pretty preprint based on the utterly physical construction of the heterotic string.
It's just remarkable that something so mathematically exceptional – by its symmetries – may be considered "another solution" to the same spacetime equations that also admit our Universe as a solution.
I still consider the \(E_8\times E_8\) heterotic string to be the most well-motivated candidate description of Nature including quantum gravity. Dualities probably admit other descriptions as well – F-theory, M-theory, braneworlds – but the heterotic string may be the "closest one" or the "most weakly coupled" among all the descriptions.
Heterotic string theory describes our Universe as a 10-dimensional spacetime occupied by weakly coupled strings whose 2-dimensional world sheet is a "hybrid" ("heterosis" is "hybrid vigor", the ability of offspring to surpass the average of both parents). The left-moving excitations on the world sheet are taken from the \(D=26\) bosonic string theory while the right-moving ones are those from the \(D=10\) fermionic string theory (with the \(\NNN=1\) world sheet supersymmetry).
Because the critical dimensions don't agree, the remaining \(D_L-D_R=26-10=16\) left-moving dimensions have to be compactified on the torus deduced from an even self-dual lattice (or fermionized to 32 fermions whose boundary conditions must be modular invariant). There are two even self-dual lattices in 16 dimensions and we obtain theories with spacetime gauge groups \(SO(32)\) or \(E_8\times E_8\). Both of them have rank \(16\) and dimension \(496\).