Expansion of EYM Amplitudes in Gauge Invariant Vector Space

Understand

Motivated by the problem of expanding single-trace tree-level amplitude of Einstein-Yang-Mills theory to the BCJ basis of Yang-Mills amplitudes, we present an alternative expansion formula in the gauge invariant vector space.

• Starting from a generic vector space consisting of polynomials of momenta and polarization vectors, we define a new sub-space as gauge invariant vector space by imposing constraints of gauge invariant conditions.
• To characterize this sub-space, we compute its dimension and construct an explicit gauge invariant basis from it.
• We propose an expansion formula in the gauge invariant basis with expansion coefficients being linear combinations of Yang-Mills amplitude, manifesting the gauge invariance of both expansion basis and coefficients.