Universal properties of superconformal OPEs for 1/2 BPS operators in $3\le D\le 6$

Abstract

We give a general analysis of OPEs of 1/2 BPS superfield operators for the $D=3,4,5,6$ superconformal algebras OSp(8/4,R), PSU(2,2), F${}_4$ and OSp($8^{\ast }/4$) which underlie maximal AdS supergravity in $4\le D+1\le 7$. \\ The corresponding three-point functions can be formally factorized in a way similar to the decomposition of a generic superconformal UIR into a product of supersingletons. This allows for a simple derivation of branching rules for primary superfields. The operators of protected conformal dimension which may appear in the OPE are classified and are shown to be either 1/2 or 1/4 BPS, or semishort. As an application, we discuss the "non-renormalization" of extremal $n$-point correlators.

To be published in NJP Focus Issue: Supersymmetry in condensed matter and high energy physics

References in corpus (10)

• Properties of the Konishi multiplet in N=4 SYM theory
• On Non-renormalization and OPE in Superconformal Field Theories
• On the OPE of 1/2 BPS Short Operators in N=4 SCFT${}_4$
• A note on composite operators in N=4 SYM
• Three-Point Functions of Quarter BPS Operators in N=4 SYM
• Superspace approach to anomalous dimensions in {\cal N}=4 SYM
• (2,0) Superconformal OPEs in D=6, Selection Rules and Non-renormalization Theorems
• (Non-)perturbative tests of the AdS/CFT correspondence
• AdS/SCFT in Superspace
• Field theory insight from the AdS/CFT correspondence

Cited by in corpus (31)

• Massless Higher Spins and Holography
• Supersymmetric Gauge Theories and the AdS/CFT Correspondence
• The $(2,0)$ superconformal bootstrap
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• On Four-Point Functions of Half-BPS Operators in General Dimensions
• Deformation quantization and superconformal symmetry in three dimensions
• Solving M-theory with the Conformal Bootstrap
• Carving Out the End of the World or (Superconformal Bootstrap in Six Dimensions)
• On Operator Mixing in N=4 SYM
• 7D Bosonic Higher Spin Theory: Symmetry Algebra and Linearized Constraints
• The M-theory Archipelago
• Non-protected operators in N=4 SYM and multiparticle states of AdS_5 SUGRA
• M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture
• Implications of Superconformal Symmetry for Interacting (2,0) Tensor Multiplets
• Invariant Differential Operators for Non-Compact Lie Algebras Parabolically Related to Conformal Lie Algebras
• ABJM at Strong Coupling from M-theory, Localization, and Lorentzian Inversion
• 6d (2,0) and M-theory at 1-loop
• AdS${}_4$/CFT${}_3$ for Unprotected Operators
• On two fermion BMN operators
• Double-Trace Flows and the Swampland
• Bootstrapping string dynamics in the 6d $\mathcal{N}=(2,0)$ theories
• Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry
• N=4 superparticle and super Yang-Mills theory in USp(4) harmonic superspace
• Regge trajectories for the (2,0) theories
• On the M5 and the AdS7/CFT6 Correspondence
• Super-Spin Chains for 6D SCFTs
• Group-Theoretical Classification of BPS and Possibly Protected States in D=4 Conformal Supersymmetry
• Fractional Multi-Trace Fields of N=4 SYM_4 from AdS/CFT
• Exact Correlators of BPS Operators from the 3d Superconformal Bootstrap
• Superconformal Block from Holographic Geometry
• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories