Abstract
We investigate the soft behaviour of scalar effective field theories (EFTs) when there is a number of distinct derivative power counting parameters, ρ1 < ρ2 < . . . < ρQ. We clarify the notion of an enhanced soft limit and use these to extend the scope of on-shell recursion techniques for scalar EFTs. As an example, we perform a detailed study of theories with two power counting parameters, ρ1 = 1 and ρ2 = 2, that include the shift symmetric generalised galileons. We demonstrate that the minimally enhanced soft limit uniquely picks out the Dirac-Born-Infeld (DBI) symmetry, including DBI galileons. For the exceptional soft limit we uniquely pick out the special galileon within the class of theories under investigation. We study the DBI galileon amplitudes more closely, verifying the validity of the recursion techniques in generating the six point amplitude, and explicitly demonstrating the invariance of all amplitudes under DBI galileon duality.
Highlights
We investigate the soft behaviour of scalar effective field theories (EFTs) when there is a number of distinct derivative power counting parameters, ρ1 < ρ2 < . . . < ρQ
We demonstrate that the minimally enhanced soft limit uniquely picks out the Dirac-Born-Infeld (DBI) symmetry, including DBI galileons
JHEP04(2017)015 since their couplings only depend on a single parameter, the structure of the interactions is protected by an enhanced symmetry that can be directly related to the soft limit using Ward identities [11]
Summary
We will briefly review the main results for single ρ theories presented in [10, 11]. This is the scalar sector of the DBI Lagrangian where the infinite number of coupling constants has been reduced to a single parameter λ. Again by equation (2.1) the first enhancement occurs when σ = 2 and demanding that the theory (2.5) realises a quadratic soft limit degree induces constraints on the coupling constants which yields the galileon Lagrangian whose form in four spacetime dimensions is [2]. Even though the cubic galileon term is invariant under the galileon symmetry, one can consistently set its co-efficient to zero without changing the theory thanks to the galileon duality [26, 27] In this sense the infinite number of coupling constants of (2.5) have been reduced to a pair of galileon coupling constants.
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