Abstract
We argue that conformal invariance is a common thread linking several scalar effective field theories that appear in the double copy and scattering equations. For a derivatively coupled scalar with a quartic ${\cal O}(p^4)$ vertex, classical conformal invariance dictates an infinite tower of additional interactions that coincide exactly with Dirac-Born-Infeld theory analytically continued to spacetime dimension $D=0$. For the case of a quartic ${\cal O}(p^6)$ vertex, classical conformal invariance constrains the theory to be the special Galileon in $D=-2$ dimensions. We also verify the conformal invariance of these theories by showing that their amplitudes are uniquely fixed by the conformal Ward identities. In these theories, conformal invariance is a much more stringent constraint than scale invariance.
Highlights
The modern scattering amplitudes program has exposed an array of extraordinary theoretical structures which include the double copy [1,2,3,4], scattering equations [5,6,7,8], and novel reformulations of amplitudes as polyhedra [9,10]
We show how the conformal Ward identities—together with Lorentz invariance, locality, factorization, and the leading Adler zero [46]—are sufficient to uniquely bootstrap these amplitudes, confirming via an amplitude analysis that the corresponding effective field theories (EFTs) are fixed by classical conformal invariance
Since DBI and the special Galileon are fixed by conformal invariance, it would be interesting to devise new on-shell recursion relations [59] which exploit this fact
Summary
The modern scattering amplitudes program has exposed an array of extraordinary theoretical structures which include the double copy [1,2,3,4], scattering equations [5,6,7,8], and novel reformulations of amplitudes as polyhedra [9,10]. Via the double copy procedure, gravity’s highly complex amplitudes can be obtained by “squaring” much simpler amplitudes from gauge theory This simplification sits at the heart of the recent state-of-art calculation of the black hole binary Hamiltonian at third post-Minkowskian order [11,12]. The same set of theories emerges again and again when studying the double-copy and scattering equations This set includes well-known theories like gravity and Yang-Mills (YM) in addition to a variety of scalar theories such as the biadjoint scalar (BS), the nonlinear sigma model (NLSM), Dirac-Born-Infeld (DBI) theory, and the special Galileon [8,13,14]. Our results are concrete examples where conformal invariance imposes further constraints beyond scale invariance
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