Happy New Year!
First, Nima Arkani-Hamed (IAS) and Jaroslav Trnka (Caltech) have released another amplituhedron preprint, Into the Amplituhedron, in which they expose the amplituhedron origin of various QFT rules applied to cuts – the unitarity double cut, the multicollinear limit (which explains why the amplitude is sometimes the exponential of something simpler), and other cuts (whose properties emerge from the shape of \(d\)-dimensional faces of the amplituhedron).
But there's another intriguing hep-th paper published on the last day of 2013 (even if we overlook the remaining dozens of papers): Thomas Faulkner, Monica Guica, Thomas Hartman, Robert C. Myers, and Mark Van Raamsdonk wrote
Gravitation from Entanglement in Holographic CFTswhich provides us with a much more constructive, microscopically complete, anti de Sitter version of Ted Jacobson's heuristic derivation of Einstein's equations from entropy considerations (see e.g. Event horizons and thermodynamics: more than analogy, TRF 2010).