In search of conformal theories

Abstract

The conformal crossing equation puts very stringent constraints on the conformal data. We formulate it in way that makes the conformal symmetry more transparent. This allows for generalization of the crossing equation to arbitrary Lie group G. Using the crossing equation for SU(2) as a toy model, we find infinitely many solutions to the G-crossing equation. In particular, when G is specialized to the conformal group SO(d+1,1), we get infinitely many solutions to the conformal crossing equation.

arXiv comment21 pages, 6 figures

References in corpus (5)

• Conformal Partial Waves and the Operator Product Expansion
• Non-commutative World-volume Geometries: Branes on SU(2) and Fuzzy Spheres
• Open Strings and Non-commutative Geometry of Branes on Group Manifolds
• The space-time operator product expansion in string theory duals of field theories
• dS/CFT and the operator product expansion

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• Conformal Basis, Optical Theorem, and the Bulk Point Singularity
• Holographic Reconstruction of AdS Exchanges from Crossing Symmetry
• On the Polyakov-Mellin bootstrap
• Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications
• Harmonic analysis of 2d CFT partition functions
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• Crossing Kernels for Boundary and Crosscap CFTs
• Double-Trace Deformations of Conformal Correlations
• Inverse Bootstrapping Conformal Field Theories
• Action principle for OPE
• The F-theorem in the melonic limit
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• Conformal Two-Point Correlation Functions from the Operator Product Expansion
• Analytic Studies of Fermions in the Conformal Bootstrap