Searching for gauge theories with the conformal bootstrap

摘要

A bstract 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 T D documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ {mathcal{T}}_D $$end{document} , which at large N approach solutions containing free fermion bilinears at ? = D ? 1 from below. The kinks T D documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ {mathcal{T}}_D $$end{document} 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 T D documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ {mathcal{T}}_D $$end{document} are subgroups of SO( N ), and we speculate that the kinks T D documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ {mathcal{T}}_D $$end{document} relate to the fixed points of gauge theories coupled to fermions.