Selected Topics in Analytic Conformal Bootstrap: A Guided Journey

Abstract

This review aims to offer a pedagogical introduction to the analytic conformal bootstrap program via a journey through selected topics. We review analytic methods which include the large spin perturbation theory, Mellin space methods and the Lorentzian inversion formula. These techniques are applied to a variety of topics ranging from large-N theories, to the epsilon expansion and holographic superconformal correlators, and are demonstrated in a large number of explicit examples.

Invited review for Physics Reports, 150 pages, 29 figures; v2: discussions improved, references added, to appear on Physics Reports

References in corpus (90)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• New Relations for Gauge-Theory Amplitudes
• Holography from Conformal Field Theory
• Conformal collider physics: Energy and charge correlations
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Writing CFT correlation functions as AdS scattering amplitudes
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Nonrelativistic conformal field theories
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Galilean Conformal Algebras and AdS/CFT
• Comments on operators with large spin
• Mellin amplitudes for $Ad{S}_5\times S^5$
• New positivity bounds from full crossing symmetry
• Sharp Boundaries for the Swampland
• Conformal Bootstrap in Mellin Space
• Extremal Effective Field Theories
• Loop Corrections to Supergravity on $Ad{S}_5\times S^5$
• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• Crossing Symmetric Dispersion Relations in QFTs
• From dS to AdS and back
• Where is String Theory?
• AdS Bulk Locality from Sharp CFT Bounds
• Gluon Scattering in AdS from CFT
• A new handle on three-point coefficients: OPE asymptotics from genus two modular invariance
• On duality of color and kinematics in (A)dS momentum space
• Recursion Relations for AdS/CFT Correlators
• Four point function of $\mathcal{N}=4$ stress-tensor multiplet at strong coupling
• Color/Kinematics Duality in AdS${}_4$
• The critical O(N) CFT: Methods and conformal data
• Superprotected n-point correlation functions of local operators in N=4 super Yang-Mills
• Double Copy Relation for AdS
• Conjectures for Large N Superconformal N=4 Chiral Primary Four Point Functions
• Crossing Symmetric Dispersion Relations for Mellin Amplitudes
• A novel representation of an integrated correlator in $\mathcal{N}=4$ SYM theory
• Cosmological Scattering Equations
• Fast Conformal Bootstrap and Constraints on 3d Gravity
• Bootstrapping the half-BPS line defect CFT in $\mathcal{N}=4$ SYM at strong coupling
• Poking Holes in AdS/CFT: Bulk Fields from Boundary States
• All Tree-Level Correlators for M-theory on $Ad{S}_7\times S^4$
• Harmonic analysis of 2d CFT partition functions
• The nuts and bolts of the BMS Bootstrap
• On the Differential Representation and Color-Kinematics Duality of AdS Boundary Correlators
• ${\mathbb{Z}}_N$ Symmetries, Anomalies, and the Modular Bootstrap
• Double copy structure of parity-violating CFT correlators
• Lightcone Bootstrap at higher points
• Gaudin Models and Multipoint Conformal Blocks: General Theory
• Four-point correlators with higher weight superconformal primaries in the AdS/CFT Correspondence
• One-loop Gluon Amplitudes in AdS
• Quantum field theory and the Bieberbach conjecture
• Monodromy Defects from Hyperbolic Space
• $\epsilon$-Expansion in Critical ${\varphi }^3$-Theory on Real Projective Space from Conformal Field Theory
• Distributions in CFT II. Minkowski Space
• Towards the Virasoro-Shapiro Amplitude in AdS5xS5
• S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem
• Fermions in AdS and Gross-Neveu BCFT
• Rigorous bounds on the Analytic $S$-matrix
• Gaudin Models and Multipoint Conformal Blocks II: Comb channel vertices in 3D and 4D
• The Virasoro-Shapiro amplitude in AdS${}_5\times$S${}^5$ and level splitting of 10d conformal symmetry
• QFT, EFT and GFT
• ABJM at Strong Coupling from M-theory, Localization, and Lorentzian Inversion
• Holographic Correlators at Finite Temperature
• Towards Color-Kinematics Duality in Generic Spacetimes
• Operator Product Expansion and Conservation Laws in Non-Relativistic Conformal Field Theories
• On Analytic Bootstrap for Interface and Boundary CFT
• Singularities of thermal correlators at strong coupling
• Resurgence of the large-charge expansion
• Gaudin Models and Multipoint Conformal Blocks III: Comb channel coordinates and OPE factorisation
• Multipoint correlators on the supersymmetric Wilson line defect CFT
• Bootstrapping Monodromy Defects in the Wess-Zumino Model
• Selection rules for the S-Matrix bootstrap
• On Galilean conformal bootstrap
• Swampland Conditions for Higher Derivative Couplings from CFT
• Perturbative and Nonperturbative Studies of CFTs with MN Global Symmetry
• Crossing antisymmetric Polyakov blocks + Dispersion relation
• Spinor-Helicity Formalism for Massless Fields in AdS${}_4$ III: Contact Four-Point Amplitudes
• More on holographic correlators: Twisted and dimensionally reduced structures
• Superconformal Boundaries in $4-\epsilon$ dimensions
• Mellin amplitudes for 1$d$ CFT
• Following the flow for large N and large charge
• Defect Conformal Blocks from Appell Functions
• Mixed Correlator Dispersive CFT Sum Rules
• Holographic S-fold theories at one loop
• On the consistency of (partially-)massless matter couplings in de Sitter space
• Snowmass White Paper: Bootstrapping String Theory
• Universal Dynamics in Non-Orientable CFT${}_2$
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Towards the non-perturbative cosmological bootstrap
• 2D CFTs - Large Charge is not enough
• Recursive structure of the Gauß hypergeometric function and boundary/crosscap conformal block

Cited by in corpus (25)

• Bootstrapping line defects with $O(2)$ global symmetry
• New Developments in the Numerical Conformal Bootstrap
• Fermions in Boundary Conformal Field Theory : Crossing Symmetry and $\epsilon$-Expansion
• AdS super gluon scattering up to two loops: A position space approach
• The Shadow Formalism of Galilean CFT${}_2$
• Bootstrapping the Kronig-Penney Model
• Spinning correlators in $\mathcal{N}=2$ SCFTs: Superspace and AdS amplitudes
• Interacting conformal scalar in a wedge
• Flat-space structure of gluon and graviton in AdS
• Spectrum of a Gross-Neveu Yukawa model with flavor disorder in $d=3$
• Bootstrapping Witten diagrams via differential representation in Mellin space
• Notes on $n$-point Witten diagrams in AdS${}_2$
• Positivity, low twist dominance and CSDR for CFTs
• Scattering bound states in AdS
• All Next-to-Next-to-Extremal One-Loop Correlators of AdS Supergluons and Supergravitons
• Bootstrapping AdS${}_2\times$ S${}^2$ hypermultiplets: hidden four-dimensional conformal symmetry
• 1d Conformal Field Theory and Dispersion Relations
• An Elliptic One-Loop Amplitude in Anti-de-Sitter Space
• A Celestial Route to AdS Bulk Locality
• Large $N$ analytical functional bootstrap I: 1D CFTs and total positivity
• Bound on the central charge of CFTs in large dimension
• Resummation of Multi-Stress Tensors in Higher Dimensions
• ANEC on stress-tensor states in perturbative $\lambda {\varphi }^4$ theory
• Universal thermalization dynamics in (1+1)d QFTs
• Bootstrap Method in Theoretical Physics