The Shadow Formalism of Galilean CFT${}_2$

Abstract

In this work, we develop the shadow formalism for two-dimensional Galilean conformal field theory (GCFT${}_2$). We define the principal series representation of Galilean conformal symmetry group and find its relation with the Wigner classification, then we determine the shadow transform of local operators. Using this formalism we derive the OPE blocks, Clebsch-Gordan kernels, conformal blocks and conformal partial waves. A new feature is that the conformal block admits additional branch points, which would destroy the convergence of OPE for certain parameters. We establish another inversion formula different from the previous one, but get the same result when decomposing the four-point functions in the mean field theory (MFT). We also construct a continuous series of bilocal actions of MFT, and an exceptional series of local actions, one of which is the BMS free scalar model. We notice that there is an outer automorphism of the Galilean conformal symmetry, and the GCFT${}_2$ can be regarded as null defect in higher dimensional CFTs.

arXiv commentpublished version, minor changes

References in corpus (89)

• 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
• The Spectrum in the Sachdev-Ye-Kitaev Model
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Writing CFT correlation functions as AdS scattering amplitudes
• 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 Bootstrap Program for Boundary CFT_d
• Nonrelativistic conformal field theories
• Ambitwistor strings and the scattering equations
• SCHRÖdinger Invariance and Strongly Anisotropic Critical Systems
• Conformal Field Theories Near a Boundary in General Dimensions
• Galilean Conformal Algebras and AdS/CFT
• Holography of 3d Flat Cosmological Horizons
• A Natural Language for AdS/CFT Correlators
• Light-ray operators in conformal field theory
• Carrollian Perspective on Celestial Holography
• BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries
• Entropy of three-dimensional asymptotically flat cosmological solutions
• A Stereoscopic Look into the Bulk
• The S-matrix Bootstrap I: QFT in AdS
• Entanglement entropy in Galilean conformal field theories and flat holography
• Warped Conformal Field Theory
• Bootstrapping the 3d Ising twist defect
• More on Supersymmetric and 2d Analogs of the SYK Model
• Classical and Quantized Tensionless Strings
• A spacetime derivation of the Lorentzian OPE inversion formula
• Scattering Amplitudes: Celestial and Carrollian
• Conformal Carroll groups
• Boundary and Interface CFTs from the Conformal Bootstrap
• Entanglement Entropy in Flat Holography
• Analytic Bounds and Emergence of ${\text{AdS}}_2$ Physics from the Conformal Bootstrap
• Weight Shifting Operators and Conformal Blocks
• $d$-dimensional SYK, AdS Loops, and $6j$ Symbols
• Chiral Scale and Conformal Invariance in 2D Quantum Field Theory
• The S-matrix Bootstrap II: Two Dimensional Amplitudes
• Field Theories with Conformal Carrollian Symmetry
• Conformal Invariance in the Long-Range Ising Model
• Recursion Relations for Conformal Blocks
• The Analytic Functional Bootstrap I: 1D CFTs and 2D S-Matrices
• The Analytic Functional Bootstrap II: Natural Bases for the Crossing Equation
• Tensionless Strings from Worldsheet Symmetries
• On the null origin of the ambitwistor string
• Universal anomalous dimensions at large spin and large twist
• Analytic bootstrap at large spin
• Harmonic Analysis and Mean Field Theory
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Conformal Blocks for Arbitrary Spins in Two Dimensions
• Crossing Symmetry in Alpha Space
• BMS Modules in Three Dimensions
• Celestial Diamonds: Conformal Multiplets in Celestial CFT
• Field Theories on Null Manifolds
• Flat space physics from AdS/CFT
• The Mellin Formalism for Boundary CFT${}_d$
• An Analytic Approach to BCFT${}_d$
• Carrollian and celestial spaces at infinity
• On Higher-dimensional Carrollian and Galilean Conformal Field Theories
• Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite $\sqrt{T\bar{T}}$ deformations
• Momentum-space conformal blocks on the light cone
• The S-matrix Bootstrap IV: Multiple Amplitudes
• The ABC (in any D) of Logarithmic CFT
• The nuts and bolts of the BMS Bootstrap
• A note on the SYK model with complex fermions
• Analytic Functional Bootstrap for CFTs in $d>1$
• Geometric actions and flat space holography
• Swing surfaces and holographic entanglement beyond AdS/CFT
• Inhomogeneous Tensionless Superstrings
• Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes
• Unitarity and positivity constraints for CFT at large central charge
• Operator Product Expansion and Conservation Laws in Non-Relativistic Conformal Field Theories
• Semi-classical BMS${}_3$ blocks and flat holography
• Modular Hamiltonians in flat holography and (W)AdS/WCFT
• Nonrelativistic Conformal Field Theories in the Large Charge Sector
• The complex null string, Galilean conformal algebra and scattering equations
• On Galilean conformal bootstrap
• Comments on Determinant Formulas for General CFTs
• Galilean Field Theories and Conformal Structure
• Conformal symmetry in non-local field theories
• BMS Modular Diaries: Torus one-point function
• More on the operator-state map in non-relativistic CFTs
• Supersymmetric Galilean conformal blocks
• Semi-classical BMS-blocks from the Oscillator Construction
• Applications of Alpha Space
• Galilean Conformal Algebra in Semi-Infinite Space

Cited by in corpus (2)

• A BMS-invariant free fermion model
• Quantization of Carrollian conformal scalar theories