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

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 $\mathcal{N}=4$ super Yang-Mills on the Coulomb branch; i.e. the Dirac-Born-Infeld action on AdS${}_5\times S^5$.

48 pages, one appendix

References in corpus (4)

• Light scalar at LHC: the Higgs or the dilaton?
• Spontaneous Breaking of Conformal Invariance and Trace Anomaly Matching
• Soft behavior of a closed massless state in superstring and universality in the soft behavior of the dilaton
• Quantum scale-invariant models as effective field theories

Cited by in corpus (13)

• Geometric Soft Theorems
• Subleading Soft Theorem for Multiple Soft Gravitons
• Scale and Weyl Invariance in Einstein-Cartan Gravity
• Exceptional scalar theories in de Sitter space
• Bootstrapping the $a$-anomaly in $4d$ QFTs
• The B-field soft theorem and its unification with the graviton and dilaton
• Quantum Corrections to Generic Branes: DBI, NLSM, and More
• Hidden Conformal Invariance of Scalar Effective Field Theories
• On the Symmetry Foundation of Double Soft Theorems
• On the EFT of Conformal Symmetry Breaking
• Topics in Asymptotic Symmetries and Infrared Effects
• Equivalence of EFTs and Time-Like Extra Dimensions
• Soft-Theorems for Scalar Particles: The Dilatons Story