Hidden order and unconventional superconductivity in URu$_2$Si$_2$

The nature of the so-called hidden order in URu$_2$Si$_2$ and the subsequent superconducting phase have remained a puzzle for over two decades. Motivated by evidence for rotational symmetry breaking seen in recent magnetic torque measurements [Okazaki et al. Science {\bf 331}, 439 (2011)], we derive a simple tight-binding model consistent with experimental Fermi surface probes and ab-initio calculations. From this model we use mean-field theory to examine the variety of hidden orders allowed by existing experimental results, including the torque measurements. We then construct a phase diagram in temperature and pressure and discuss relevant experimental consequences.