Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 10, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP10(2021)160
Keywords
Conformal and W Symmetry; Conformal Field Theory
Categories
Funding
- Simons Foundation [488651]
- DOE [DE-SC0020318, DESC0017660]
- NSERC
- U.S. Department of Energy (DOE) [DE-SC0020318] Funding Source: U.S. Department of Energy (DOE)
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In this study, we focus on 5-point functions in conformal field theories with dimensions greater than 2. By utilizing weight-shifting operators, we are able to derive recursion relations that simplify the computation of arbitrary conformal blocks in 5-point functions involving scalar operators, reducing them to a linear combination of blocks with scalar exchanges. Additionally, we establish recursion relations for the conformal blocks with spin 1 or 2 in the context of 5-point functions, allowing for the formulation of positivity constraints related to the expectation value of the energy operator in bilocal states created by two scalars.
We consider 5-point functions in conformal field theories in d > 2 dimensions. Using weight-shifting operators, we derive recursion relations which allow for the computation of arbitrary conformal blocks appearing in 5-point functions of scalar operators, reducing them to a linear combination of blocks with scalars exchanged. We additionally derive recursion relations for the conformal blocks which appear when one of the external operators in the 5-point function has spin 1 or 2. Our results allow us to formulate positivity constraints using 5-point functions which describe the expectation value of the energy operator in bilocal states created by two scalars.
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