Charging Up the Functional Bootstrap

Abstract

We revisit the problem of bootstrapping CFT correlators of charged fields. After discussing in detail how bounds for uncharged fields can be recycled to the charged case, we introduce two sets of analytic functional bases for correlators on the line. The first, which we call "simple", is essentially a direct sum of analytic functionals for the uncharged case. We use it to establish very general bounds on the OPE density appearing in charged correlators. The second basis is dual to generalized free fields and we explain how it is related to a charged version of the Polyakov bootstrap. We apply these functionals to map out the space of correlators and obtain new improved bounds on the 3d Ising twist defect.

arXiv comment44 pages, 8 figures, typos corrected, minor details added, references added

References in corpus (27)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Bootstrapping the O(N) Vector Models
• Bootstrapping the 3d Ising twist defect
• A Mellin space approach to the conformal bootstrap
• Bootstrapping the O(N) Archipelago
• Conformal Bootstrap in Mellin Space
• Analytic Bounds and Emergence of ${\text{AdS}}_2$ Physics from the Conformal Bootstrap
• Crossing Symmetric Dispersion Relations in QFTs
• The Analytic Functional Bootstrap I: 1D CFTs and 2D S-Matrices
• The Analytic Functional Bootstrap II: Natural Bases for the Crossing Equation
• A Study of Quantum Field Theories in AdS at Finite Coupling
• On the Polyakov-Mellin bootstrap
• Nonperturbative Mellin Amplitudes: Existence, Properties, Applications
• An Analytic Approach to BCFT${}_d$
• Mellin space bootstrap for global symmetry
• Recursion Relations in Witten Diagrams and Conformal Partial Waves
• Crossing Symmetric Dispersion Relations for Mellin Amplitudes
• On critical exponents without Feynman diagrams
• JuliBootS: a hands-on guide to the conformal bootstrap
• Analytic Functional Bootstrap for CFTs in $d>1$
• A Crossing-Symmetric OPE Inversion Formula
• Crossing symmetry, transcendentality and the Regge behaviour of 1d CFTs
• The O(N) S-matrix Monolith
• Applications of dispersive sum rules: $\epsilon$-expansion and holography
• Cut-touching linear functionals in the conformal bootstrap
• Aspects of CFTs on Real Projective Space
• A Basis of Analytic Functionals for CFTs in General Dimension

Cited by in corpus (5)

• Positivity and Geometric Function Theory Constraints on Pion Scattering
• Towards Bootstrapping RG flows: Sine-Gordon in AdS
• Crossing antisymmetric Polyakov blocks + Dispersion relation
• Locality and Analyticity of the Crossing Symmetric Dispersion Relation
• Large $N$ analytical functional bootstrap I: 1D CFTs and total positivity