Gravity as the Square of Gauge Theory

The BCJ squaring relations provide a simple prescription for the computation of gravity amplitudes in terms of gauge theory ingredients. Unlike the KLT relations, the squaring relations are directly applicable both at tree and loop level. We review the derivation of these relations from on-shell recursion relations, and discuss an off-shell approach to these relations in which the interactions of the gravity Lagrangian arise as the square of the gauge-theory interactions. This article is based on work with Zvi Bern, Tristan Dennen and Yu-tin Huang [Z. Bern, T. Dennen, Y.-t. Huang and M. Kiermaier, Phys. Rev. D 82 (2010), 065003, arXiv:1004.0693 (Ref. 1))] which was presented at String Field Theory and Related Aspects 2010.