Soft theorems for boosts and other time symmetries

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.

arXiv comment50 pages

References in corpus (83)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Generalized Global Symmetries
• The Effective Field Theory of Inflation
• Quantum Contributions to Cosmological Correlations
• On BMS Invariance of Gravitational Scattering
• Single field consistency relation for the 3-point function
• BMS supertranslations and Weinberg's soft graviton theorem
• Starting the Universe: Stable Violation of the Null Energy Condition and Non-standard Cosmologies
• On graviton non-Gaussianities during inflation
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• New Symmetries of Massless QED
• Horizon crossing and inflation with large η
• Null energy condition and superluminal propagation
• Adiabatic Modes in Cosmology
• On Soft Limits of Inflationary Correlation Functions
• Implications of conformal invariance in momentum space
• Effective Field Theories from Soft Limits
• Effective field theory for hydrodynamics: thermodynamics, and the derivative expansion
• On the consistency relation of the 3-point function in single field inflation
• Conformal consistency relations for single-field inflation
• Single-Field Consistency Relations of Large Scale Structure
• Symmetries and Consistency Relations in the Large Scale Structure of the Universe
• The Cosmological Bootstrap: Weight-Shifting Operators and Scalar Seeds
• Conformal Symmetries of Adiabatic Modes in Cosmology
• A Periodic Table of Effective Field Theories
• Relativistic Fluids, Superfluids, Solids and Supersolids from a Coset Construction
• Galilean invariance and the consistency relation for the nonlinear squeezed bispectrum of large scale structure
• An Infinite Set of Ward Identities for Adiabatic Modes in Cosmology
• Improved Estimates of Cosmological Perturbations
• The Cosmological Optical Theorem
• Spontaneous Symmetry Breaking and Nambu-Goldstone Bosons in Quantum Many-Body Systems
• CMB from CFT
• Cosmological Cutting Rules
• Operator Product Expansion of Inflationary Correlators and Conformal Symmetry of de Sitter
• Symmetries and Loops in Inflation
• Conformal Invariance and the Four Point Scalar Correlator in Slow-Roll Inflation
• Building a Boostless Bootstrap for the Bispectrum
• Linking the Singularities of Cosmological Correlators
• Cutting Cosmological Correlators
• From Locality and Unitarity to Cosmological Correlators
• On Loops in Inflation III: Time Independence of zeta in Single Clock Inflation
• A Hidden Symmetry of the Galileon
• Stability of Geodesically Complete Cosmologies
• Conformal invariance of scalar perturbations in inflation
• Ward Identities for Scale and Special Conformal Transformations in Inflation
• Conformal $n$-point functions in momentum space
• Boostless Cosmological Collider Bootstrap
• One-particle-irreducible consistency relations for cosmological perturbations
• On Squeezed Limits in Single-Field Inflation - Part I
• Goldstone modes and photonization for higher form symmetries
• Cosmological Bootstrap in Slow Motion
• Slavnov-Taylor Identities for Primordial Perturbations
• Noether's Second Theorem and Ward Identities for Gauge Symmetries
• Shapes of gravity: Tensor non-Gaussianity and massive spin-2 fields
• Soft Theorems For Shift-Symmetric Cosmologies
• Superfluids as Higher-form Anomalies
• A generalized non-Gaussian consistency relation for single field inflation
• Inflationary Consistency Conditions from a Wavefunctional Perspective
• Cosmological Scattering Equations
• Bootstrapping Large Graviton non-Gaussianities
• Spontaneous Symmetry Probing
• The Conformal Limit of Inflation in the Era of CMB Polarimetry
• From Amplitudes to Contact Cosmological Correlators
• Soft-Pion Theorems for Large Scale Structure
• Inflationary soft theorems revisited: A generalized consistency relation
• The Effective Theory of Shift-Symmetric Cosmologies
• A Differential Representation of Cosmological Wavefunctions
• Symmetric Superfluids
• Generalized Symmetries of the Graviton
• The Cosmological Phonon: Symmetries and Amplitudes on Sub-Horizon Scales
• Multiple Soft Limits of Cosmological Correlation Functions
• Systematics of Adiabatic Modes: Flat Universes
• Soft pion theorem, asymptotic symmetry and new memory effect
• Double Soft Limits of Cosmological Correlations
• Spontaneously broken boosts and the Goldstone continuum
• Non-Trivial Checks of Novel Consistency Relations
• On Graviton non-Gaussianities in the Effective Field Theory of Inflation
• Effective Field Theory of non-Attractor Inflation
• Solid Consistency
• Solid Soft Theorems
• A non-perturbative test of consistency relations and their violation
• Squeezing $f_{\mathrm{NL}}$ out of the matter bispectrum with consistency relations
• Spatial Curvature at the Sound Horizon

Cited by in corpus (4)

• Bootstrapping Multi-Field Inflation: non-Gaussianities from light scalars revisited
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• No time to derive: unraveling total time derivatives in in-in perturbation theory
• Soft Phonon Theorems