Abstract
Infrared fixed points of gauge theories provide intriguing targets for the modern conformal bootstrap program. In this work we provide some preliminary evidence that a family of gauged fermionic CFTs saturate bootstrap bounds and can potentially be solved with the conformal bootstrap. We start by considering the bootstrap for SO(N) vector 4-point functions in general dimension D. In the large N limit, upper bounds on the scaling dimensions of the lowest SO(N) singlet and traceless symmetric scalars interpolate between two solutions at ∆ = D/2 − 1 and ∆ = D − 1 via generalized free field theory. In 3D the critical O(N) vector models are known to saturate the bootstrap bounds and correspond to the kinks approaching ∆ = 1/2 at large N. We show that the bootstrap bounds also admit another infinite family of kinks \( {\mathcal{T}}_D \), which at large N approach solutions containing free fermion bilinears at ∆ = D − 1 from below. The kinks \( {\mathcal{T}}_D \) appear in general dimensions with a D-dependent critical N* below which the kink disappears. We also study relations between the bounds obtained from the bootstrap with SO(N) vectors, SU(N) fundamentals, and SU(N) × SU(N) bi-fundamentals. We provide a proof for the coincidence between bootstrap bounds with different global symmetries. We show evidence that the proper symmetries of the underlying theories of \( {\mathcal{T}}_D \) are subgroups of SO(N), and we speculate that the kinks \( {\mathcal{T}}_D \) relate to the fixed points of gauge theories coupled to fermions.
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Li, Z., Poland, D. Searching for gauge theories with the conformal bootstrap. J. High Energ. Phys. 2021, 172 (2021). https://doi.org/10.1007/JHEP03(2021)172
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DOI: https://doi.org/10.1007/JHEP03(2021)172