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Title:
Recursion Relations for Five-Point Conformal Blocks and Beyond: A Practical Approach
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Abstract:
In this talk, I will consider five-point functions in conformal field theories (CFTs) in d > 2 spacetime dimensions. I will put forward a concrete and practical approach to computing global conformal blocks that appear in 5-point functions of arbitrary scalar operators in general CFTs. By exploiting the weight-shifting operator formalism, I will construct a simple set of recursion relations for generating five-point blocks for arbitrary symmetric traceless exchange, which may be utilized to reduce such blocks to linear combinations of scalar exchange blocks with shifted external dimensions. Throughout, I will restrict attention to parity-even five-point functions in parity-preserving CFTs. Our results may be seen as a natural generalization of the work of Dolan and Osborn to the 5-point case. Moving beyond the external scalar case, I will consider how to promote one of the external scalars to a spin-1 or a spin-2 operator. I will show a way to derive
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