Searching for gauge theories with the conformal bootstrap

Li, Zhijin; Poland, David

doi:10.1007/jhep03(2021)172

Title: Searching for gauge theories with the conformal bootstrap

Journal Article · Thu Mar 18 00:00:00 EDT 2021 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep03(2021)172· OSTI ID:1853574

^[1]; Poland, David ^[1]

Yale Univ., New Haven, CT (United States)

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 Δ = D/2 – 1 and Δ = 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 Δ = 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 Δ = 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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Research Organization:: Yale Univ., New Haven, CT (United States)

Sponsoring Organization:: USDOE Office of Science (SC); Simons Foundation

Grant/Contract Number:: SC0020318; 488651

OSTI ID:: 1853574

Journal Information:: Journal of High Energy Physics (Online), Vol. 2021, Issue 3; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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