QCD equation of state at large baryon chemical potential
In plain words
Supercomputer calculations of QCD work well at zero net density but fail at high density because of the sign problem (contributions of opposite sign that cancel almost exactly). Without a fix, the dense part of the phase diagram cannot be computed directly.
Precise statement
Compute the pressure $P(T,\mu_{B})$ and the chiral transition line of $2+1$-flavor QCD at physical quark masses for $\mu_{B}/T$ between 3 and 6 with controlled continuum extrapolation, despite the complex fermion determinant. Answer: $P$ and $T_{\mathrm{pc}}(\mu_{B})$ with percent-level uncertainty, by any method (reweighting, Taylor expansion, imaginary $\mu_{B}$, complex Langevin, Lefschetz thimbles) validated against established results at $\mu_{B}/T<2$.
What would settle it
An algorithm with cost polynomial in the lattice volume, validated against established results at $\mu_B/T < 2$ and applied at $\mu_B/T = 3\ \text{to}\ 6$.