2d small N=4 Long-multiplet superconformal block

Abstract

We study 2d N=4 superconformal field theories, focusing on its application on numerical bootstrap study. We derive the superconformal block by utilizing the global part of the super Virasoro algebra and set up the crossing equations for the non-BPS long-multiplet 4-point function. Along the way, we build global N=4 superconformal short and long multiplets, and compute all possible 2,3-point functions of long-multiplets that are needed to construct the superconformal blocks and the crossing equations. Since we consider a long-multiplet 4-point function, the number of crossing equations is huge and we expect it to give a strong constraint than the usual superconformal bootstrap analysis, which relies on BPS 4-point functions. In addition, we present an alternative way to derive crossing equations using N=4 superspace and comment on a puzzle.

40 pages. Mathematica files attached; v3: a final version to appear in JHEP, with minor corrections

References in corpus (7)

• Bootstrapping Mixed Correlators in the 3D Ising Model
• More on Supersymmetric and 2d Analogs of the SYK Model
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Holomorphic reduction of N=2 gauge theories, Wilson-'t Hooft operators, and S-duality
• VOAs labelled by complex reflection groups and 4d SCFTs
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Cited by in corpus (7)

• Bootstrapping line defects in $\mathcal{N}=2$ theories
• Superconformal Blocks: General Theory
• Spin 2 fluctuations in 1/4 BPS AdS${}_3$/CFT${}_2$
• On generalised D1-D5 near horizons and their spectra
• Twisted holography on AdS${}_3\times S^3\times K3$ & the planar chiral algebra
• Harmonic Analysis in d-dimensional Superconformal Field Theory
• Crossing Symmetry for Long Multiplets in 4D $\mathcal{N}=1$ SCFTs