An Atlas for 3d Conformal Field Theories with a U(1) Global Symmetry

Samuel Bartlett-Tisdall; Christopher P. Herzog; Vladimir Schaub

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arXiv · 2412.01608

An Atlas for 3d Conformal Field Theories with a U(1) Global Symmetry

Samuel Bartlett-Tisdall·Christopher P. Herzog·Vladimir Schaub

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Abstract

We present a collection of numerical bootstrap computations for 3d CFTs with a U(1) global symmetry. We test the accuracy of our method and fix conventions through a computation of bounds on the OPE coefficients for low-lying operators in the free fermion, free scalar, and generalised free vector field theories. We then compute new OPE bounds for scalar operators in the Gross-Neveu-Yukawa model, $O(2)$ model, and large $N$ limit of the $O(N)$ model. Additionally, we present a number of exclusion plots for such 3d CFTs. In particular, we look at the space of even and odd parity scalar operators in the low-lying spectrum that are compatible with crossing symmetry. As well as recovering the known theories, there are some kinks that indicate new unknown theories.

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BibTeX RIS

Samuel Bartlett-Tisdall, Christopher P. Herzog, Vladimir Schaub. 2025-04-25. An Atlas for 3d Conformal Field Theories with a U(1) Global Symmetry. https://arxiv.org/abs/2412.01608

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