Swampland Conditions for Higher Derivative Couplings from CFT

Abstract

There are effective field theories that cannot be embedded in any UV complete theory. We consider scalar effective field theories, with and without dynamical gravity, in $D$-dimensional anti-de Sitter (AdS) spacetime with large radius and derive precise bounds (analytically) on the coupling constants of higher derivative interactions ${\varphi }^2{\square }^k{\varphi }^2$ by only requiring that the dual CFT obeys the standard conformal bootstrap axioms. In particular, we show that all such coupling constants, for even $k\ge 2$, must satisfy positivity, monotonicity, and log-convexity conditions in the absence of dynamical gravity. Inclusion of gravity only affects constraints involving the ${\varphi }^2{\square }^2{\varphi }^2$ interaction which now can have a negative coupling constant. Our CFT setup is a Lorentzian four-point correlator in the Regge limit. We also utilize this setup to derive constraints on effective field theories of multiple scalars. We argue that similar analysis should impose nontrivial constraints on the graviton four-point scattering amplitude in AdS.

37 pages + appendices, multiple figures

References in corpus (40)

• On the Geometry of the String Landscape and the Swampland
• Causality, Analyticity and an IR Obstruction to UV Completion
• The Swampland: Introduction and Review
• Holography from Conformal Field Theory
• Conformal collider physics: Energy and charge correlations
• Writing CFT correlation functions as AdS scattering amplitudes
• The String Landscape and the Swampland
• Lectures on the Swampland Program in String Compactifications
• The EFT-Hedron
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Positive Moments for Scattering Amplitudes
• New positivity bounds from full crossing symmetry
• Sharp Boundaries for the Swampland
• Extremal Effective Field Theories
• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• Crossing Symmetric Dispersion Relations in QFTs
• Where is String Theory?
• Bounds for OPE coefficients on the Regge trajectory
• Gluon Scattering in AdS from CFT
• S-matrix Bootstrap for Effective Field Theories: Massless Pions
• Landau diagrams in AdS and S-matrices from conformal correlators
• Causality in Curved Spacetimes: The Speed of Light & Gravity
• Bounds on OPE Coefficients from Interference Effects in the Conformal Collider
• Carving out the Space of Open-String S-matrix
• Positivity in Multi-Field EFTs
• A Bound on Massive Higher Spin Particles
• Elastic positivity vs extremal positivity bounds in SMEFT: a case study in transversal electroweak gauge-boson scatterings
• Quantum field theory and the Bieberbach conjecture
• Positivity in electron-positron scattering: testing the axiomatic quantum field theory principles and probing the existence of UV states
• Dual S-matrix Bootstrap I: 2D Theory
• S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem
• Selection rules for the S-Matrix bootstrap
• The S-matrix Bootstrap III: Higher Dimensional Amplitudes
• Scattering from production in 2d
• Closed Strings and Weak Gravity from Higher-Spin Causality
• Lessons from crossing symmetry at large N
• Causality Constraints in Large $N$ QCD Coupled to Gravity
• All-Order Quartic Couplings in Highly Symmetric D-brane-Anti-D-brane Systems
• Gravitational Positivity Bounds on Scalar Potentials
• EFT of 6D SUSY RG Flows

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• Analyticity and Unitarity for Cosmological Correlators
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• Into the EFThedron and UV constraints from IR consistency
• Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds
• Exploring The Holographic Swampland
• Triple crossing positivity bounds for multi-field theories
• Positivity and Geometric Function Theory Constraints on Pion Scattering
• Moments for positivity: using Drell-Yan data to test positivity bounds and reverse-engineer new physics
• Subleading Bounds on Chaos
• Extremal Chaos
• Mixed Correlator Dispersive CFT Sum Rules
• Locality and Analyticity of the Crossing Symmetric Dispersion Relation
• Positivity bounds at one-loop level: the Higgs sector
• A Celestial Route to AdS Bulk Locality