Hidden Orbital Order in $URu_{2}Si_{2}$

When matter is cooled from high temperatures, collective instabilities develop amongst its constituent particles that lead to new kinds of order. An anomaly in the specific heat is a classic signature of this phenomenon. Usually the associated order is easily identified, but sometimes its nature remains elusive. The heavy fermion metal $URu_2Si_2$ is one such example, where the order responsible for the sharp specific heat anomaly at $T_0=17 K$ has remained unidentified despite more than seventeen years of effort. In $URu_{2}Si_{2}$, the coexistence of large electron-electron repulsion and antiferromagnetic fluctuations in $URu_2Si_2$ leads to an almost incompressible heavy electron fluid, where anisotropically paired quasiparticle states are energetically favored. In this paper we use these insights to develop a detailed proposal for the hidden order in $URu_2Si_2$. We show that incommensurate orbital antiferromagnetism, associated with circulating currents between the uranium ions, can account for the local fields and entropy loss observed at the $17 K$ transition; furthermore we make detailed predictions for neutron scattering measurements.