On Galilean conformal bootstrap

Abstract

In this work, we develop conformal bootstrap for Galilean conformal field theory (GCFT). In a GCFT, the Hilbert space could be decomposed into quasiprimary states and its global descendants. Different from the usual conformal field theory, the quasi-primary states in a GCFT constitute multiplets, which are block-diagonized under the Galilean boost operator. More importantly the multiplets include the states of negative norms, indicating the theory is not unitary. We compute global blocks of the multiplets, and discuss the expansion of four-point functions in terms of the global blocks of the multiplets. Furthermore we do the harmonic analysis for the Galilean conformal symmetry and obtain an inversion formula. As the first step to apply the Galilean conformal bootstrap, we construct generalized Galilean free theory (GGFT) explicitly. We read the data of GGFT by using Taylor series expansion of four-point function and the inversion formula independently, and find exact agreement. We discuss some novel features in the Galilean conformal bootstrap, due to the non-semisimpleness of the Galilean conformal algebra and the non-unitarity of the GCFTs.

arXiv comment75 pages, 2 figures, 4 tables; v2: references added, typos corrected; v3: references added, typos corrected, new appendices added

References in corpus (68)

• Comments on the Sachdev-Ye-Kitaev model
• Bounding scalar operator dimensions in 4D CFT
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Holography from Conformal Field Theory
• Solving the 3D Ising Model with the Conformal Bootstrap
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Writing CFT correlation functions as AdS scattering amplitudes
• Logarithmic Operators in Conformal Field Theory
• The Analytic Bootstrap and AdS Superhorizon Locality
• Analyticity in Spin in Conformal Theories
• Convexity and Liberation at Large Spin
• Projectors, Shadows, and Conformal Blocks
• The BMS/GCA correspondence
• Galilean Conformal Algebras and AdS/CFT
• OPE Convergence in Conformal Field Theory
• Holography of 3d Flat Cosmological Horizons
• A Natural Language for AdS/CFT Correlators
• Large Spin Perturbation Theory
• BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries
• Entropy of three-dimensional asymptotically flat cosmological solutions
• Unitarity and the Holographic S-Matrix
• Entanglement entropy in Galilean conformal field theories and flat holography
• Warped Conformal Field Theory
• More on Supersymmetric and 2d Analogs of the SYK Model
• GCA in 2d
• A spacetime derivation of the Lorentzian OPE inversion formula
• Conformal Bootstrap in Mellin Space
• Non-relativistic conformal symmetries and Newton-Cartan structures
• Entanglement Entropy in Flat Holography
• Analytic Bounds and Emergence of ${\text{AdS}}_2$ Physics from the Conformal Bootstrap
• Chiral Scale and Conformal Invariance in 2D Quantum Field Theory
• Exotic Galilean Conformal Symmetry and its Dynamical Realisations
• On Representations and Correlation Functions of Galilean Conformal Algebras
• Logarithmic Conformal Field Theory: Beyond an Introduction
• The Conformal Bootstrap at Finite Temperature
• The Analytic Functional Bootstrap I: 1D CFTs and 2D S-Matrices
• The Analytic Functional Bootstrap II: Natural Bases for the Crossing Equation
• Universal anomalous dimensions at large spin and large twist
• Analytic bootstrap at large spin
• A tauberian theorem for the conformal bootstrap
• Harmonic Analysis and Mean Field Theory
• Conformal Blocks for Arbitrary Spins in Two Dimensions
• Universality at large transverse spin in defect CFT
• Crossing Symmetry in Alpha Space
• Flat space physics from AdS/CFT
• Comments on Galilean conformal field theories and their geometric realization
• The BMS Bootstrap
• Analytic Euclidean Bootstrap
• The ABC (in any D) of Logarithmic CFT
• Primary Fields in Celestial CFT
• Logarithmic conformal field theories as limits of ordinary CFTs and some physical applications
• Singular Vectors in Logarithmic Conformal Field Theories
• The nuts and bolts of the BMS Bootstrap
• Analytic Functional Bootstrap for CFTs in $d>1$
• A Crossing-Symmetric OPE Inversion Formula
• Swing surfaces and holographic entanglement beyond AdS/CFT
• Operator Product Expansion in Logarithmic Conformal Field Theory
• Unitarity and positivity constraints for CFT at large central charge
• Bootstrapping holographic warped CFTs or: how I learned to stop worrying and tolerate negative norms
• Semi-classical BMS${}_3$ blocks and flat holography
• Modular Hamiltonians in flat holography and (W)AdS/WCFT
• 2d Galilean Field Theories with Anisotropic Scaling
• BMS Characters and Modular Invariance
• Supersymmetric Warped Conformal Field Theory
• Logarithmic correlators or responses in non-relativistic analogues of conformal invariance
• Applications of Alpha Space
• Operator Algebra in Logarithmic Conformal Field Theory
• Analytic Bootstrap for Logarithmic CFT

Cited by in corpus (13)

• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• On Higher-dimensional Carrollian and Galilean Conformal Field Theories
• A BMS-invariant free scalar model
• Intrinsic Approach to $1+1$D Carrollian Conformal Field Theory
• Aspects of Non-Relativistic Quantum Field Theories
• A BMS-invariant free fermion model
• Schrödinger symmetry: a historical review
• The Shadow Formalism of Galilean CFT${}_2$
• Quantization of Carrollian conformal scalar theories
• Bulk Reconstruction of Scalar Excitations in Flat${}_3$/CCFT${}_2$ and the Flat Limit from (A)dS${}_3$/CFT${}_2$
• Thermal Corrections to Rényi Entropy in BMS Field Theory
• Character of the highest weight module of BMS algebra realized on codimensional-two boundary
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory