2017/09/30 by Simone Giombi, Eric Perlmutter
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Class (philosophy) #Computation #Conformal field theory #Conformal map #Field (mathematics) #Flow (mathematics) #Homotopy and Cohomology in Algebraic Topology #Interpretation (philosophy) #Order (exchange) #Spin (aerodynamics) #hep-th
paper · pdf · doi:10.1007/jhep03(2018)026
25+13 pages. v2: refs added, minor clarifications
arxiv created 2017/10/04 · openalex created_date 2017/10/06 · openalex publication_date 2018/03/01 · arxiv updated 2018/04/04 · openalex updated_date 2026/08/06
A bstract We explore the idea that large N , non-supersymmetric conformal field theories with a parametrically large gap to higher spin single-trace operators may be obtained as infrared fixed points of relevant double-trace deformations of superconformal field theories. After recalling the AdS interpretation and some potential pathologies of such flows, we introduce a concrete example that appears to avoid them: the ABJM theory at finite k , deformed by ∫ O2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mstyle> <mml:mo>∫</mml:mo> <mml:mrow> <mml:msup> <mml:mi>O</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:mstyle> </mml:math> , where O <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> is the superconformal primary in the stress-tensor multiplet. We address its relation to recent conjectures based on weak gravity bounds, and discuss the prospects for a wider class of similarly viable flows. Next, we proceed to analyze the spectrum and correlation functions of the putative IR CFT, to leading non-trivial order in 1 /N . This includes analytic computations of the change under double-trace flow of connected four-point functions of ABJM superconformal primaries; and of the IR anomalous dimensions of infinite classes of double-trace composite operators. These would be the first analytic results for anomalous dimensions of finite-spin composite operators in any large N CFT 3 with an Einstein gravity dual.