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Multiplets of Superconformal Symmetry in Diverse Dimensions
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Multiplets of Superconformal Symmetry in Diverse Dimensions
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We systematically analyze the operator content of unitary superconformal multiplets in $d > 3$ spacetime dimensions. We present a simple, general, and efficient algorithm that generates all of these multiplets by correctly eliminating possible null states. The algorithm is conjectural, but passes a vast web of consistency checks. We apply it to tabulate a large variety of superconformal multiplets. In particular, we classify and construct all multiplets that contain conserved currents or free fields, which play an important role in superconformal field theories (SCFTs). Some currents that are allowed in conformal field theories cannot be embedded in superconformal multiplets, and hence they are absent in SCFTs. We use the structure of superconformal stress tensor multiplets to show that SCFTs with more than 16 Poincar\'e supercharges cannot arise in $d \geq 4$, even when the corresponding superconformal algebras exist. We also show that such theories do arise in $d = 3$, but are necessarily free.
Forward citations
Cited by 8 Pith papers
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BPS Non-Renormalization in the BMN Matrix Model
Conjugation deformations preserve normalizability in the BMN matrix model, implying BPS states do not lift and their unsigned number is invariant except at the free and BFSS points.
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Holographic constraint on AdS vacua is violated for Z2 orbifolds but restored by non-abelian extensions, implying O-planes cannot wrap cycles in distinct homology classes.
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A note on the holographic consistency of DGKT-type vacua with $h^{2,1}=0$
Cancellations that satisfy a holographic three-point function constraint in DGKT vacua persist across examples with h^{2,1}=0 and more complicated triple-intersection numbers.
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