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.
Highlights
On the other hand, a large class of CFTs in higher dimensions are realized through gauge interactions
We show that the bootstrap bounds admit another infinite family of kinks TD, which at large N approach solutions containing free fermion bilinears at ∆ = D − 1 from below
These results lead to two immediate questions: from the numerical bootstrap point of view, why do we always have such a drastic symmetry enhancement? And going back to the kinks we found in figure 3, assuming these kinks relate to full-fledged theories, are the enhanced SO(2N ) vector (SO)(N ) global symmetries physical or just caused by the bootstrap algorithm?
Summary
Different from the critical 3D Ising model [4], the operators that we observe decoupling from spectrum near the family of kinks TD usually have high scaling dimensions (∆ ∼ 17 for N = 18, Λ = 31) which are not very well converged. For N = 18, below which the bootstrap bound becomes relatively smooth, the traceless symmetric scalar at the kink location ∆φ ∼ (1.75, 1.8) approaches marginality, ∆T 4,10 while the lowest singlet scalar stays irrelevant. This is based on the observation that the ∆φ of the kink, compared with ∆S,T , is more stable to increasing Λ. We will give additional discussion on this point after clarifying several aspects of the 4D results
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