Abstract
We construct entangled states of gluons that scatter exactly as if they were gravitons. Operationally, these objects implement the double copy at the level of the wave function. Our analysis begins with a general ansatz for a wave function characterizing gluons in two copies of SU(N ) gauge theory. Given relatively minimal assumptions following from permutation invariance and dimensional analysis, the three- and four-particle wave functions generate scattering amplitudes that automatically coincide exactly with gravity, modulo normalization. For five-particle scattering the match is not automatic but imposing certain known selection rules on the amplitude is sufficient to uniquely reproduce gravity. The resulting amplitudes exhibit a color-dressed and permutation-invariant form of the usual double copy relations. We compute the entanglement entropy between the two gauge theory copies and learn that these states are maximally-entangled at large N . Moreover, this approach extends immediately to effective field theories, where Born-Infeld photons and Galileons can be similarly recast as entangled gluons and pions.
Highlights
For all of these reasons, we pursue a more bottom-up approach
We ask, under what conditions does this entangled gluon state, evolving by the independent dynamics prescribed by each gauge theory copy, scatter exactly as if it were a collection of gravitons? As it turns out, for three- and four-particle scattering, any choice of entanglement ansatz produces the known amplitudes for gravitons, dilatons, and two-forms up to overall normalization
We present a set of remarkably simple entangled gluon states that reproduce three, four, and five-graviton scattering
Summary
We attempt to formalize eq (1.1) into an explicit equation mapping graviton states to entangled gluon states in a double copy Hilbert space, HYM ⊗ HYM We choose both gauge theory factors to have the same gauge group SU(N ). The entanglement ansatz in eq (2.6) implicitly assumes that color indices are only contracted across copies, i.e., that no YM color indices are contracted with each other and for YM We make this choice to draw a parallel with the structure of Kaluza-Klein theories, where the graviphoton states that are identified as gluons carry internal color indices that link up with the indices of the Killing vector generators on an internal manifold. The entanglement kernel K is, a priori, a general function of the permutation σ and the external momenta p It can be constrained since we require Bose symmetry on the gravitons. By applying eq (2.8), we can obtain K for all other members of that conjugacy class
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