Mysteries & Myriad Challenges of Finite Density Field Theory

Strongly interacting matter is described by Quantum Chromo Dynamics (QCD), the theory of interactions of quarks and gluons. Its phase diagram in the temperature-baryon density plane is being explored actively both theoretically and experimentally. Quantum field theory at nonzero temperatures and densities provides the requisite tool, with QCD on a space-time lattice as the most reliable technique to address the necessary non-perturbative aspects. While significant results have already been obtained at zero density, one stumbles upon both mysteries and myriad challenges in attempts to extend to finite densities. My talk will focus on some of them that have been missed out so far.