2015/03/31 by Nikolay Bobev, Sheer El-Showk, Dalimil Mazáč +2 · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Central charge #Conformal anomaly #Conformal field theory #Conformal map #Dimension (graph theory) #Formalism (music) #Mathematical analysis #Mathematical physics #Mathematics #Multiplet #Operator product expansion #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Spacetime #Superpotential #Supersymmetry #Theoretical physics #Unitarity #cond-mat.stat-mech #cond-mat.str-el #hep-th
paper · pdf · doi:10.1007/jhep08(2015)142
published as JHEP 1508 (2015) 142 · 43+16 pages, 13 figures. Comments welcome. v2: Minor changes, published version
openalex publication_date 2015/08/01 · arxiv created 2015/08/28 · arxiv updated 2015/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the constraints imposed by superconformal symmetry, crossing symmetry, and unitarity for theories with four supercharges in spacetime dimension 2 ≤ d ≤ 4. We show how superconformal algebras with four Poincaré supercharges can be treated in a formalism applicable to any, in principle continuous, value of d and use this to construct the superconformal blocks for any d ≤ 4. We then use numerical bootstrap techniques to derive upper bounds on the conformal dimension of the first unprotected operator appearing in the OPE of a chiral and an anti-chiral superconformal primary. We obtain an intriguing structure of three distinct kinks. We argue that one of the kinks smoothly interpolates between the d = 2, N=(2, 2) minimal model with central charge c = 1 and the theory of a free chiral multiplet in d = 4, passing through the critical Wess-Zumino model with cubic superpotential in intermediate dimensions.