# Double-soft behavior of the dilaton of spontaneously broken conformal invariance

## TL;DR

This paper derives and confirms the double-soft behavior of dilatons in spontaneously broken conformal invariance, showing it can be obtained by sequential single-soft limits, through both perturbative and nonperturbative methods.

## Contribution

It establishes a new double-soft theorem for dilatons in conformal field theories, connecting it to single-soft limits and confirming it via multiple approaches.

## Key findings

- Double-soft behavior equals two sequential single-soft limits.
- Confirmed the theorem at tree-level in a conformal field theory.
- Validated the theorem nonperturbatively using AdS/CFT correspondence.

## Abstract

The Ward identities involving the currents associated to the spontaneously broken scale and special conformal transformations are derived and used to determine, through linear order in the two soft-dilaton momenta, the double-soft behavior of scattering amplitudes involving two soft dilatons and any number of other particles. It turns out that the double-soft behavior is equivalent to performing two single-soft limits one after the other. We confirm the new double-soft theorem perturbatively at tree-level in a $D$-dimensional conformal field theory model, as well as nonperturbatively by using the "gravity dual'' of ${\cal{N}}=4$ super Yang-Mills on the Coulomb branch; i.e. the Dirac-Born-Infeld action on AdS${}_5 \times S^5$.