Fermion conformal bootstrap in 4d. (English) Zbl 1416.81158
Summary: We apply numerical conformal bootstrap techniques to the four-point function of a Weyl spinor in 4d non-supersymmetric CFTs. We find universal bounds on operator dimensions and OPE coefficients, including bounds on operators in mixed symmetry representations of the Lorentz group, which were inaccessible in previous bootstrap studies. We find discontinuities in some of the bounds on operator dimensions, and we show that they arise due to a generic yet previously unobserved “fake primary” effect, which is related to the existence of poles in conformal blocks. We show that this effect is also responsible for similar discontinuities found in four-fermion bootstrap in 3d, as well as in the mixed-correlator analysis of the 3d Ising CFT. As an important byproduct of our work, we develop a practical technology for numerical approximation of general 4d conformal blocks.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81T16 | Nonperturbative methods of renormalization applied to problems in quantum field theory |
| 83C60 | Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism |
Keywords:
conformal field theory; field theories in higher dimensions; nonperturbative effects; Weyl spinorReferences:
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