Abstract
We derive soft theorems for theories in which time symmetries — symmetries that involve the transformation of time, an example of which are Lorentz boosts — are spontaneously broken. The soft theorems involve unequal-time correlation functions with the insertion of a soft Goldstone in the far past. Explicit checks are provided for several examples, including the effective theory of a relativistic superfluid and the effective field theory of inflation. We discuss how in certain cases these unequal-time identities capture information at the level of observables that cannot be seen purely in terms of equal-time correlators of the field alone. We also discuss when it is possible to phrase these soft theorems as identities involving equal-time correlators.
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Hui, L., Joyce, A., Komissarov, I. et al. Soft theorems for boosts and other time symmetries. J. High Energ. Phys. 2023, 123 (2023). https://doi.org/10.1007/JHEP02(2023)123
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DOI: https://doi.org/10.1007/JHEP02(2023)123