Abstract
We derive closed-form expressions for all ingredients of the Zamolodchikov-like recursion relation for general spinning conformal blocks in 3-dimensional conformal field theory. This result opens a path to efficient automatic generation of conformal block tables, which has immediate applications in numerical conformal bootstrap program. Our derivation is based on an understanding of null states and conformally-invariant differential operators in momentum space, combined with a careful choice of the relevant tensor structures bases. This derivation generalizes straightforwardly to higher spacetime dimensions d, provided the relevant Clebsch-Gordan coefficients of Spin (d) are known.
Highlights
The conformal bootstrap [1,2,3] has resurfaced as a powerful tool by numerically constraining the algebra of local operators in conformal field theories (CFTs) in d > 2 space-time dimensions [4]
Most of the numerical bootstrap studies to date focused on crossing equations for four-point functions of scalar operators, which turned out to be sufficient to significantly constrain and, to some extent, numerically solve interesting conformal field theories
Beyond providing universal constraints on the CFTs that include fermionic operators [6,7,8], a conserved current [9], or a stress-energy tensor [10], the analysis of four-point functions of spinning-operators has provided access to specific theories which have proven hard to study by only analyzing scalar correlators
Summary
The conformal bootstrap [1,2,3] has resurfaced as a powerful tool by numerically constraining the algebra of local operators in conformal field theories (CFTs) in d > 2 space-time dimensions [4] (for a recent review see [5]). Most of the numerical bootstrap studies to date focused on crossing equations for four-point functions of scalar operators, which turned out to be sufficient to significantly constrain and, to some extent, numerically solve interesting conformal field theories. In order to place further constraints on the space of unitary CFTs, the analysis of four-point functions that include spinning operators has proven fruitful. Beyond providing universal constraints on the CFTs that include fermionic operators [6,7,8], a conserved current [9], or a stress-energy tensor [10], the analysis of four-point functions of spinning-operators has provided access to specific theories which have proven hard to study by only analyzing scalar correlators. One would like a computer program which, given the parameters of a conformal block, would automatically produce an approximation of the block suitable for use in numerical bootstrap algorithms
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
