Abstract
Exceptional theories are a group of one-parameter scalar field theories with (enhanced) vanishing soft limits in the S-matrix elements. They include the nonlinear sigma model (NLSM), Dirac-Born-Infeld scalars and the special Galileon theory. The soft behavior results from the shift symmetry underlying these theories, which leads to Ward identities generating subleading single soft theorems as well as novel Berends-Giele recursion relations. Such an approach was first applied to NLSM in refs. [1, 2], and here we use it to systematically study other exceptional scalar field theories. In particular, using the subleading single soft theorem for the special Galileon we identify the Feynman vertices of the corresponding extended theory, which was first discovered using the Cachazo-He-Yuan representation of scattering amplitudes. Furthermore, we present a Lagrangian for the extended theory of the special Galileon, which has a rich particle content involving biadjoint scalars, Nambu-Goldstone bosons and Galileons, as well as additional flavor structure.
Highlights
Infinity [19, 20]
The on-shell amplitudes of nonlinear sigma model (NLSM), DBI and special Galileon possess non-trivial single soft limits, which are known to be related to the underlying shift symmetry of the theories
We performed a systematic analysis of these theories using quantum fieldtheoretic methods, by deriving the Ward identities associated with the shift symmetry
Summary
It has long been recognized that the Adler’s zero in scattering amplitudes of NGBs can be derived from current conservation corresponding to the nonlinear shift symmetry. Current conservation corresponding to the shift symmetry leads to the Ward identity:. The discussion above can be generalized to scalars with flavor, e.g. in NLSM, or enhanced soft limit, e.g. in DBI, ordinary Galileon and special Galileon. The case for general enhanced Adler’s zero has been discussed in [27]. It is clear from our discussion that to get the leading order soft theorem, one needs to calculate the remainder function Rμ(p) to the lowest order in p. We will realize this idea for NLSM, DBI, ordinary Galileon and special Galileon
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