A method is presented to derive conformal blocks for arbitrary Lorentz representations using predetermined substitutions on Gegenbauer polynomials after determining relevant group structures.
Recursion Relations for Conformal Blocks
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abstract
In the context of conformal field theories in general space-time dimension, we find all the possible singularities of the conformal blocks as functions of the scaling dimension $\Delta$ of the exchanged operator. In particular, we argue, using representation theory of parabolic Verma modules, that in odd spacetime dimension the singularities are only simple poles. We discuss how to use this information to write recursion relations that determine the conformal blocks. We first recover the recursion relation introduced in 1307.6856 for conformal blocks of external scalar operators. We then generalize this recursion relation for the conformal blocks associated to the four point function of three scalar and one vector operator. Finally we specialize to the case in which the vector operator is a conserved current.
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Review of so(1,D) representations for de Sitter space across all D, covering mixed symmetry and fermions, connected to propagating fields.
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Conformal Four-Point Correlation Functions from the Operator Product Expansion
A method is presented to derive conformal blocks for arbitrary Lorentz representations using predetermined substitutions on Gegenbauer polynomials after determining relevant group structures.
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QFT as a set of ODEs: higher dimensions
Generalizes flow ODEs for QFT data in AdS3/AdS4, capturing operator merger-annihilation and level repulsion, with efficiency gains from crossing equations and Padé approximants.
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De Sitter Representations
Review of so(1,D) representations for de Sitter space across all D, covering mixed symmetry and fermions, connected to propagating fields.