Nonrelativistic effective field theories with enhanced symmetries and soft behavior

Abstract

We systematically explore the landscape of nonrelativistic effective field theories with a local $S$-matrix and enhanced symmetries and soft behavior. The exploration is carried out using both conventional quantum field theory methods based on symmetry arguments, and recently developed on-shell recursion relations. We show that, in contrary to relativistic theories, enhancement of the soft limit of scattering amplitudes in nonrelativistic theories is generally not a byproduct of symmetry alone, but requires additional low-energy data. Sufficient conditions for enhanced scattering amplitudes can be derived by combining symmetries and dispersion relations of the scattered particles. This has direct consequences for the infrared dynamics that different types of nonrelativistic Nambu-Goldstone bosons can exhibit. We then use a bottom-up soft bootstrap approach to narrow down the landscape of nonrelativistic effective field theories that possess a consistent low-energy $S$-matrix. We recover two exceptional theories of a complex Schrödinger-type scalar, namely the $\mathbb{C}{P}^1$ nonlinear sigma model and the Schrödinger-Dirac-Born-Infeld theory. Moreover, we use soft recursion to prove a no-go theorem ruling out the existence of other exceptional Schrödinger-type theories. We also prove that all exceptional theories of a single real scalar with a linear dispersion relation are necessarily Lorentz-invariant. Soft recursion allows us to obtain some further general bounds on the landscape of nonrelativistic effective theories with enhanced soft limits. Finally, we present a novel theory of a complex scalar with a technically natural quartic dispersion relation. Altogether, our work represents the first step of a program to extend the developments in the study of scattering amplitudes to theories without Lorentz invariance.

arXiv comment67 pages, 3 figures

References in corpus (56)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• New Recursion Relations for Tree Amplitudes of Gluons
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Scattering of Massless Particles in Arbitrary Dimension
• On the Foundations of Chiral Perturbation Theory
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• Asymptotic Symmetries of Yang-Mills Theory
• Spontaneously Broken Spacetime Symmetries and Goldstone's Theorem
• The EFT-Hedron
• Effective Field Theories from Soft Limits
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Nonrelativistic effective Lagrangians
• On-Shell Recursion Relations for Effective Field Theories
• Operator bases, $S$-matrices, and their partition functions
• A Periodic Table of Effective Field Theories
• Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
• Hilbert series and operator bases with derivatives in effective field theories
• Redundancies in Nambu-Goldstone Bosons
• Extensions of Theories from Soft Limits
• Unifying Relations for Scattering Amplitudes
• Celestial Amplitudes from UV to IR
• Effective Lagrangian for Nonrelativistic Systems
• A Hidden Symmetry of the Galileon
• Soft Bootstrap and Supersymmetry
• Higher-spin massless S-matrices in four-dimensions
• Vector Effective Field Theories from Soft Limits
• Spontaneous breaking of spacetime symmetries and the inverse Higgs effect
• Scalar Field Theories with Polynomial Shift Symmetries
• Recursion relations from soft theorems
• Criterion for stability of Goldstone Modes and Fermi Liquid behavior in a metal with broken symmetry
• Scattering Amplitudes from Soft Theorems and Infrared Behavior
• New Soft Theorems for Goldstone Boson Amplitudes
• Soft Bootstrap and Effective Field Theories
• Goldstones with Extended Shift Symmetries
• Geometry of Special Galileon
• Lie-algebraic classification of effective theories with enhanced soft limits
• Probing Scalar Effective Field Theories with the Soft Limits of Scattering Amplitudes
• Ward Identity and Scattering Amplitudes for Nonlinear Sigma Models
• The Infrared Structure of Nambu-Goldstone Bosons
• An Algebraic Classification of Exceptional EFTs
• Multicritical Symmetry Breaking and Naturalness of Slow Nambu-Goldstone Bosons
• Effective Lagrangians for quantum many-body systems
• Shift symmetries, soft limits, and the double copy beyond leading order
• Double Copy in Higher Derivative Operators of Nambu-Goldstone Bosons
• New Flavor-Kinematics Dualities and Extensions of Nonlinear Sigma Models
• Cascading Multicriticality in Nonrelativistic Spontaneous Symmetry Breaking
• On the Supersymmetrization of Galileon Theories in Four Dimensions
• Symmetry Realization via a Dynamical Inverse Higgs Mechanism
• Multi-spin soft bootstrap and scalar-vector Galileon
• Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory
• Noether currents of locally equivalent symmetries
• Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
• Scattering Amplitudes and Soft Theorems in Multi-Flavor Galileon Theories
• On-Shell Recursion Relations for Nonrelativistic Effective Field Theories
• Exceptional nonrelativistic effective field theories with enhanced symmetries

Cited by in corpus (7)

• Aspects of Non-Relativistic Quantum Field Theories
• Effective Field Theory for Spontaneously Broken Symmetry
• Inflationary Adler Conditions
• A Well-Posed UV Completion for Simulating Scalar Galileons
• Soft Phonon Theorems
• Fractional soft limits
• Geometric duality between effective field theories I: scattering amplitudes