Systematics of Quarter BPS operators in N=4 SYM

Abstract

A systematic construction is presented of 1/4 BPS operators in N=4 superconformal Yang-Mills theory, using either analytic superspace methods or components. In the construction, the operators of the classical theory annihilated by 4 out of 16 supercharges are arranged into two types. The first type consists of those operators that contain 1/4 BPS operators in the full quantum theory. The second type consists of descendants of operators in long unprotected multiplets which develop anomalous dimensions in the quantum theory. The 1/4 BPS operators of the quantum theory are defined to be orthogonal to all the descendant operators with the same classical quantum numbers. It is shown, to order $g^2$, that these 1/4 BPS operators have protected dimensions.

arXiv comment27 pages. Minor changes to text and references

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• $20^{\prime }$ Five-Point Function from $Ad{S}_5\times S^5$ Supergravity
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• Non-planar Anomalous Dimensions in the sl(2) Sector
• Superconformal partial waves in Grassmannian field theories
• Cut-and-join operators and N=4 super Yang-Mills
• Quarter BPS classified by Brauer algebra
• On instanton contributions to anomalous dimensions in N=4 supersymmetric Yang-Mills theory
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• Positive Energy Unitary Irreducible Representations of the Superalgebras osp(1|2n,R)
• Geometry of Higgs-branch superconformal primary bundles
• Multi giant graviton systems, SUSY breaking and CFT
• N=4 superparticle and super Yang-Mills theory in USp(4) harmonic superspace
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• Characters of the Positive Energy UIRs of D=4 Conformal Supersymmetry
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• BPS Condensates, Matrix Models and Emergent String Theory
• Negative anomalous dimensions in N=4 SYM
• Group-Theoretical Classification of BPS and Possibly Protected States in D=4 Conformal Supersymmetry
• Group-Theoretical Classification of BPS States in D=4 Conformal Supersymmetry: the Case of (1/N)-BPS
• Rebooting quarter-BPS operators in $\mathcal{N}=4$ Super Yang-Mills