2021/07/26 by Damon J. Binder, Daniel Z. Freedman, Silviu S. Pufu +1
Mathematics · Physics and Astronomy · #Algorithm #Black Holes and Theoretical Physics #Combinatorics #Cosmology and Gravitation Theories #Dual polyhedron #Field (mathematics) #Geometry #Massless particle #Mathematical physics #Mathematics #Multiplet #Nonlinear Waves and Solitons #Particle physics #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Rank (graph theory) #Scalar (mathematics) #Scaling #Spectral line #TRACE (psycholinguistics) #hep-th
paper · pdf · doi:10.1007/jhep01(2022)171
81 pages
arxiv created 2021/07/26 · openalex publication_date 2022/01/01 · arxiv updated 2022/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A bstract We study which bulk couplings contribute to the S 3 free energy F ( \mathfrakm <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>m</mml:mi> </mml:math> ) of three-dimensional N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 superconformal field theories with holographic duals, potentially deformed by boundary real-mass parameters m. In particular, we show that F ( \mathfrakm <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>m</mml:mi> </mml:math> ) is independent of a large class of bulk couplings that include non-chiral F-terms and all D-terms. On the other hand, in general, F ( \mathfrakm <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>m</mml:mi> </mml:math> ) does depend non-trivially on bulk chiral F-terms, such as prepotential interactions, and on bulk real-mass terms. These conclusions can be reached solely from properties of the AdS super-algebra, \mathfrakosp <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>osp</mml:mi> </mml:math> (2|4). We also consider massive vector multiplets in AdS, which in the dual field theory correspond to long single-trace superconformal multiplets of spin zero. We provide evidence that F ( \mathfrakm <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>m</mml:mi> </mml:math> ) is insensitive to the vector multiplet mass and to the interaction couplings between the massive vector multiplet and massless ones. In particular, this implies that F ( \mathfrakm <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>m</mml:mi> </mml:math> ) does not contain information about scaling dimensions or OPE coefficients of single-trace long scalar N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 superconformal multiplets.