Searching for gauge theories with the conformal bootstrap

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 TD, which at large N approach solutions containing free fermion bilinears at = D - 1 from below. The kinks TD 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) x 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 TD are subgroups of SO(N), and we speculate that the kinks TD relate to the fixed points of gauge theories coupled to fermions.

Automated summary

The study provides preliminary evidence that a class of gauged fermionic CFTs can potentially be solved with the conformal bootstrap and satisfy bootstrap bounds. The research demonstrates that the critical O(N) vector models in 3D satisfy the bootstrap bounds and are associated with kinks approaching = 1/2 at large N. Additionally, the bootstrap bounds also include another infinite family of kinks TD, which approach solutions containing free fermion bilinears at = D - 1 as N becomes large.