Abstract
We use supershadow methods to derive new expressions for superconformal blocks in 4d $\mathcal{N}=1$ superconformal field theories. We analyze the four-point function $\langle\mathcal{A}_1 \mathcal{A}_2^\dagger \mathcal{B}_1 \mathcal{B}_2^\dagger\rangle$, where $\mathcal{A}_i$ and $\mathcal{B}_i$ are scalar superconformal primary operators with arbitrary dimension and $R$-charge and the exchanged operator is neutral under $R$-symmetry. Previously studied superconformal blocks for chiral operators and conserved currents are special cases of our general results.
Highlights
Spectrum make the approach even more powerful
We analyze the four-point function A1A†2B1B2†, where Ai and Bi are scalar superconformal primary operators with arbitrary dimension and R-charge and the exchanged operator is neutral under R-symmetry
A crucial ingredient in the superconformal bootstrap is the expansion of four-point functions in superconformal blocks, which sum up the contributions of all of the descendants of a given superconformal primary operator
Summary
The superembedding formalism provides a simple language for writing down and classifying superconformally invariant correlation functions in N = 1 SCFTs [41,42,43,44,45,46,47,48,49,50]. Correlators are given by products of simple invariants. This space has a natural action of the superconformal group given by matrix multiplication on the SU(2, 2|1) indices A. PC denotes the fermion number parity of the index C (1 if C = 5, and 0 otherwise).1 By construction, these invariants are chiral in unbarred coordinates and anti-chiral in barred coordinates. Αj Poincare where the subscript “Poincare” means we choose the Poincare section gauge fixing (2.5)
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