Aspects of N=4 SYM

Abstract

The properties of gauge-invariant composite operators and their correlation functions in N=4 SYM are discussed in the analytic superspace formalism. A complete classification of the different types of operators in the theory is given. Operators can be either protected or unprotected according to whether they do not or do have anomalous dimensions, and the analytic superspace formalism allows one to identify which type a given operator is in a straightforward manner. A simple discussion is given of the behaviour of reducible multiplets at threshold. It is pointed out that there is a class of ``semi-protected'' operators which do not have anomalous dimensions but which do not necessarily have non-renormalised three-point functions when the other two operators in the correlator are protected, although two-point functions of such operators are non-renormalised. A complete discussion of superconformal invariants in analytic superspace is given. The paper includes a modified discussion of the transformation rules of analytic superfields which clarifies the $U(1{)}_Y$ properties of operators and correlation functions and, in particular, explicit examples are given of three-point correlation functions which violate this symmetry. A tensor, $\cE$, invariant under $SL(n|m)$ but not under $GL(n|m)$, is introduced and used in the discussion of $U(1{)}_Y$ and in the construction of invariants.

49 pages. Added reference and acknowledgements

References in corpus (7)

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• On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
• On stringy AdS_5 x S^5 and higher spin holography
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• Four-point functions in N=4 SYM
• Systematics of Quarter BPS operators in N=4 SYM
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• $20^{\prime }$ Five-Point Function from $Ad{S}_5\times S^5$ Supergravity
• Higher Spin Symmetry and N=4 SYM
• Unmixing Supergravity
• The super-correlator/super-amplitude duality: Part II
• N=4 Superconformal Characters and Partition Functions
• All three-loop four-point correlators of half-BPS operators in planar N=4 SYM
• More on La Grande Bouffe: towards higher spin symmetry breaking in AdS
• Supersymmetry of Tensionless Rotating Strings in AdS_5 x S^5, and Nearly-BPS Operators
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• Invariants and divergences in half-maximal supergravity theories
• Spin bit models from non-planar N=4 SYM
• Aspects of superconformal field theories in six dimensions
• Surprises from the Resolution of Operator Mixing in N = 4 SYM
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• On correlation functions of BPS operators in $3d$ $\mathcal{N}=6$ superconformal theories
• Superconformal partial waves in Grassmannian field theories
• Some remarks on (super)-conformal Killing-Yano tensors
• Operator mixing and three-point functions in N=4 SYM
• Higher spin symmetry (breaking) in N=4 SYM theory and holography
• Notes on Super Killing Tensors
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• N=4 super-Yang-Mills in LHC superspace. Part II: Non-chiral correlation functions of the stress-tensor multiplet
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