Comments on 1/16 BPS Quantum States and Classical Configurations

Abstract

We formulate the problem of counting 1/16 BPS states of N = 4 Yang Mills theory as the enumeration of the local cohomology of an operator acting on holomorphic fields on C^2. We study aspects of the enumeration of this cohomology at finite N, especially for operators constructed only out of products of covariant derivatives of scalar fields, and compare our results to the states obtained from the quantization of giant gravitons and dual giants. We physically interpret the holomorphic fields that enter our conditions for supersymmetry semi-classically by deriving a set of Bogomolnyi equations for 1/16-BPS bosonic field configurations in N = 4 Yang Mills theory on R^4 with reality properties and boundary conditions appropriate to radial quantization. An arbitrary solution to these equations in the free theory is parameterized by holomorphic data on C^2 and lifts to a nearby solution of the interacting Bogomolnyi equations only when the constraints equivalent to Q cohomology are obeyed.

61 pages

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• AdS${}_5$ Black Hole Entropy near the BPS Limit
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• Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index
• Decoding stringy near-supersymmetric black holes
• Aspects of Non-Relativistic Quantum Field Theories
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• Interacting Giant Gravitons from Spin Matrix Theory
• Exact QFT duals of AdS black holes
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• Counting Wobbling Dual-Giants
• Holomorphic field theories and Calabi--Yau algebras
• Semi-Chiral Operators in 4d $\mathcal{N}=1$ Gauge Theories
• Indices for 6 dimensional superconformal field theories
• The Panorama of Spin Matrix Theory
• An Index for Ray Operators in 5d $E_n$ SCFTs
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• Black hole microstates and supersymmetric localization
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• Fortuity and Supergravity
• More on BPS States in N=4 Supersymmetric Yang-Mills Theory on R x S3
• On BPS Strings in $\mathcal{N}=4$ Yang-Mills Theory
• Holomorphic primary fields in free CFT4 and Calabi-Yau orbifolds
• Witten index of BMN matrix quantum mechanics
• Symmetry structure of the interactions in near-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
• Loop Corrected Supercharges from Holomorphic Anomalies
• Off-shell phase diagram of BPS black holes in AdS${}_5$