A Periodic Table of Effective Field Theories

Abstract

We systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local S-matrix. To do so we define an EFT classification based on four parameters characterizing 1) the number of derivatives per interaction, 2) the soft properties of amplitudes, 3) the leading valency of the interactions, and 4) the spacetime dimension. Carving out the allowed space of EFTs, we prove that exceptional EFTs like the non-linear sigma model, Dirac-Born-Infeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Using on-shell momentum shifts and recursion relations, we prove that EFTs with arbitrarily soft behavior are forbidden and EFTs with leading valency much greater than the spacetime dimension cannot have enhanced soft behavior. We then enumerate all single scalar EFTs in d<6 and verify that they correspond to known theories in the literature. Our results suggest that the exceptional theories are the natural EFT analogs of gauge theory and gravity because they are one-parameter theories whose interactions are strictly dictated by properties of the S-matrix.

arXiv comment54 pages, 4 figures, 2 tables; v3 matched to JHEP version

References in corpus (66)

• The galileon as a local modification of gravity
• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• New Relations for Gauge-Theory Amplitudes
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• New Recursion Relations for Tree Amplitudes of Gluons
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• On BMS Invariance of Gravitational Scattering
• Scattering of Massless Particles in Arbitrary Dimension
• BMS supertranslations and Weinberg's soft graviton theorem
• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• The Amplituhedron
• What is the Simplest Quantum Field Theory?
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Gravity as the Square of Gauge Theory
• Local Integrals for Planar Scattering Amplitudes
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• New Symmetries of Massless QED
• Semiclassical Virasoro Symmetry of the Quantum Gravity S-Matrix
• A Duality For The S Matrix
• Asymptotic Symmetries of Yang-Mills Theory
• Ambitwistor strings and the scattering equations
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Evidence for a New Soft Graviton Theorem
• On the Tree-Level S-Matrix of Yang-Mills Theory
• Effective Field Theories from Soft Limits
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Low's Subleading Soft Theorem as a Symmetry of QED
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Loop Integrands for Scattering Amplitudes from the Riemann Sphere
• 2D Kac-Moody Symmetry of 4D Yang-Mills Theory
• On-Shell Recursion Relations for Effective Field Theories
• Into the Amplituhedron
• The S-Matrix in Twistor Space
• Factorization Properties of Soft Graviton Amplitudes
• Hexagon functions and the three-loop remainder function
• Consistency Conditions on the S-Matrix of Massless Particles
• Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
• One-loop amplitudes on the Riemann sphere
• Extensions of Theories from Soft Limits
• A Hidden Symmetry of the Galileon
• Gravity from Rational Curves
• Magnetic Corrections to the Soft Photon Theorem
• On-Shell Recursion Relations for Generic Theories
• Amplitude Relations in Non-linear Sigma Model
• Tree-level Amplitudes in the Nonlinear Sigma Model
• On-shell constructibility of tree amplitudes in general field theories
• Higher-spin massless S-matrices in four-dimensions
• OPE for all Helicity Amplitudes
• New Double Soft Emission Theorems
• Simple Recursion Relations for General Field Theories
• Spontaneous breaking of spacetime symmetries and the inverse Higgs effect
• Recursion relations from soft theorems
• Scalar Field Theories with Polynomial Shift Symmetries
• Gravity in Twistor Space and its Grassmannian Formulation
• Aspects of Galileon Non-Renormalization
• Recursion Relations for Tree-level Amplitudes in the SU(N) Non-linear Sigma Model
• Double Soft Theorems and Shift Symmetry in Nonlinear Sigma Models
• Unification of Galileon Dualities
• Goldstones with Extended Shift Symmetries
• On single and double soft behaviors in NLSM
• Collinear limits beyond the leading order from the scattering equations
• Double-soft behavior for scalars and gluons from string theory
• Determination of Boundary Contributions in Recursion Relation
• Boundary Operators of BCFW Recursion Relation

Cited by in corpus (119)

• New positivity bounds from full crossing symmetry
• Operator bases, $S$-matrices, and their partition functions
• Beyond Amplitudes' Positivity and the Fate of Massive Gravity
• Classical and Quantum Results on Logarithmic Terms in the Soft Theorem in Four Dimensions
• Unifying Relations for Scattering Amplitudes
• Symmetry and Action for Flavor-Kinematics Duality
• Massive Galileon Positivity Bounds
• Soft Bootstrap and Supersymmetry
• Logarithmic Terms in the Soft Expansion in Four Dimensions
• BMS Supertranslations and Not So Soft Gravitons
• Effective Field Theory Amplitudes the On-Shell Way: Scalar and Vector Couplings to Gluons
• Semi-abelian Z-theory: NLSM+phi^3 from the open string
• The electroweak effective field theory from on-shell amplitudes
• Vector Effective Field Theories from Soft Limits
• Sub-subleading Soft Graviton Theorem in Generic Theories of Quantum Gravity
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Locality and Unitarity from Singularities and Gauge Invariance
• ZZ and Zgamma still haven't found what they are looking for
• Covariant Color-Kinematics Duality
• Gravity Waves from Soft Theorem in General Dimensions
• Scattering Amplitudes from Soft Theorems and Infrared Behavior
• Pions as Gluons in Higher Dimensions
• The Rise of SMEFT On-shell Amplitudes
• Enumerating higher-dimensional operators with on-shell amplitudes
• Geometric Soft Theorems
• Shift Symmetries in (Anti) de Sitter Space
• Soft Theorems in Superstring Theory
• Subleading Soft Theorem for Multiple Soft Gravitons
• Geometry-Kinematics Duality
• Subleading Soft Graviton Theorem for Loop Amplitudes
• Renormalization Group Evolution from On-shell SMEFT
• UV considerations on scattering amplitudes in a web of theories
• New Soft Theorems for Goldstone Boson Amplitudes
• Soft Bootstrap and Effective Field Theories
• Bootstrapping two-loop Feynman integrals for planar N=4 sYM
• Lie-algebraic classification of effective theories with enhanced soft limits
• Geometry of Special Galileon
• Symmetric Superfluids
• Complete NLO Operators in the Higgs Effective Field Theory
• Probing Scalar Effective Field Theories with the Soft Limits of Scattering Amplitudes
• Maximal $U(1{)}_Y$-violating $n$-point correlators in $\mathcal{N}=4$ super-Yang-Mills theory
• The order $p^8$ mesonic chiral Lagrangian
• Amplitude bases in generic EFTs
• The Infrared Structure of Nambu-Goldstone Bosons
• Soft Matters, or the Recursions with Massive Spinors
• The Cosmological Phonon: Symmetries and Amplitudes on Sub-Horizon Scales
• An Algebraic Classification of Exceptional EFTs
• Uniqueness from gauge invariance and the Adler zero
• On the exactness of soft theorems
• An EFT hunter's guide to two-to-two scattering: HEFT and SMEFT on-shell amplitudes
• Shift symmetries, soft limits, and the double copy beyond leading order
• Universal Imprints of a Pseudo-Nambu-Goldstone Higgs Boson
• Hidden zeros are equivalent to enhanced ultraviolet scaling and lead to unique amplitudes in Tr(${\varphi }^3$) theory
• Algebraic branch points at all loop orders from positive kinematics and wall crossing
• Testing Subleading Multiple Soft Graviton Theorem for CHY Prescription
• Scalar Fields Near Compact Objects: Resummation versus UV Completion
• Six-pion amplitude
• Operator Counting and Soft Blocks in Chiral Perturbation Theory
• On the Supersymmetrization of Galileon Theories in Four Dimensions
• Symmetric Scalars
• General Relativity from Causality
• One-loop renormalization in Galileon effective field theory
• Enhanced Soft Limits in de Sitter Space
• Constructing on-shell operator basis for all masses and spins
• Soft limits of the wavefunction in exceptional scalar theories
• Taming higher-derivative interactions and bootstrapping gravity with soft theorems
• The Infrared Structure of Exceptional Scalar Theories
• Universal Relations in Composite Higgs Models
• All-Multiplicity One-Loop Amplitudes in Born-Infeld Electrodynamics from Generalized Unitarity
• Electromagnetic Duality and D3-Brane Scattering Amplitudes Beyond Leading Order
• Higher-order tree-level amplitudes in the nonlinear sigma model
• Multi-spin soft bootstrap and scalar-vector Galileon
• Constructing Generic Effective Field Theory for All Masses and Spins
• Nonrelativistic effective field theories with enhanced symmetries and soft behavior
• The ChPT: top-down and bottom-up
• Shift-Symmetric Spin-1 Theories
• Quantum Corrections to Generic Branes: DBI, NLSM, and More
• Effective Field Theory for Spontaneously Broken Symmetry
• Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector
• Noether currents of locally equivalent symmetries
• Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles
• A No-go Theorem for a Gauge Vector as a Space-time Goldstone
• Inflationary Adler Conditions
• Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
• Geometry of Multi-Flavor Galileon-Like Theories
• Matter Couplings and Equivalence Principles for Soft Scalars
• Soft theorems for boosts and other time symmetries
• Hidden Conformal Invariance of Scalar Effective Field Theories
• Soft Phonon Theorems
• Scattering Amplitudes and Soft Theorems in Multi-Flavor Galileon Theories
• Flavour-kinematics duality for Goldstone modes
• Scattering amplitudes of massive Nambu-Goldstone bosons
• Non-linearly realized discrete symmetries
• On the Symmetry Foundation of Double Soft Theorems
• D3-Brane Loop Amplitudes from M5-Brane Tree Amplitudes
• Leading soft theorem for multiple gravitini
• FiniteFieldSolve: Exactly Solving Large Linear Systems in High-Energy Theory
• Shift Symmetries for p-Forms and Mixed Symmetry Fields on (A)dS
• Special Galileon at one loop
• An Algebraic Classification of Exceptional EFTs Part II: Supersymmetry
• Fractional soft limits
• ALPs, the on-shell way
• Shift Symmetries and AdS/CFT
• Fermionic Shift Symmetries in (Anti) de Sitter Space
• Internal Supersymmetry and Small-field Goldstini
• UV consistency conditions for CHY integrands
• Soft Limits of Gluon and Graviton Correlators in Anti-de Sitter Space
• Non-perturbative aspects of galileon duality
• Exceptional nonrelativistic effective field theories with enhanced symmetries
• Symmetry Breaking Patterns for Inflation
• On the Conformal Symmetry of Exceptional Scalar Theories
• Non-perturbative quantum Galileon in the exact renormalization group
• Surface Gauge Invariance, Soft Limits and the Transmutation of Gluons into Scalars
• Symmetry and Unification from Soft Theorems and Unitarity
• New Exceptional EFTs in de Sitter Space from Generalised Energy Conservation
• Smooth Splitting and Zeros from On-Shell Recursion
• Soft unification of exceptional effective field theories in de Sitter space
• Extended DBI and its generalizations from graded soft theorems
• Geometric duality between effective field theories I: scattering amplitudes