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Bootstrapping 3D Conformal Field Theories with Product Analytic Functionals

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arxiv 2608.06497 v1 pith:3UX3Q4PW submitted 2026-08-06 hep-th

Kausik Ghosh , Zechuan Zheng This is my paper · ORCID
classification hep-th
keywords analyticdimensionexternalfunctionalsproductbasisconformalsingle
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We introduce a bootstrap method for three-dimensional conformal field theories based on product analytic functionals. The construction combines one-dimensional analytic functionals with dimensional reduction and provides an efficient alternative to the standard derivative basis. We benchmark the method in single correlator gap maximization problems for scalar and spin-two operators. At comparable basis size, the product functional basis gives stronger bounds and converges more rapidly, with the improvement becoming especially pronounced at large external dimension. Setting the external dimension to that of the three-dimensional Ising spin operator, we substantially sharpen the single correlator upper bound on the leading scalar dimension. We also sharpen the Nakayama-Ohtsuki necessary condition for critical points accessible by tuning a single parameter. In the spin-two problem, we find a new kink near $\Delta_\phi \simeq 4.16$, accompanied by a reorganization of the extremal spectrum. We also observe plateau structures at larger external dimension in both gap-maximization problems. Our results make product analytic functionals a promising tool for conformal gauge theories with heavy external operators and for probing the flat-space limit of holographic correlators; accessing both of these scenarios is challenging for conventional methods.

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