A Weakly Coupled Ultraviolet Completion of the Littlest Higgs with   T-parity
  We construct a weakly coupled, renormalizable ultraviolet completion of the Littlest Higgs model with T-parity (LHT), based on an SU(5)xSU(2)xU(1) gauge theory with a discrete Z_2 symmetry. Our model reproduces the complete structure of the LHT below the 10 TeV scale, including the collective symmetry breaking mechanism which solves the little hierarchy problem. The model is manifestly free of anomalies, including both gauge/gravitational anomalies and anomalies involving T-parity. At the TeV scale, the model contains additional states not present in the LHT. We estimate the impact of these states on precision electroweak observables, and show that the model is realistic. We also discuss how our model can be embedded into a supersymmetric theory or a five-dimensional setup with a warped extra dimension, stabilyzing the hierarchy between the 10 TeV and the Planck scale. 
Csaba Csaki, Johannes Heinonen, Maxim Perelstein and Christian   Spethmann