N=4 Superconformal Characters and Partition Functions

Abstract

Character formulae for positive energy unitary representations of the N=4 superconformal group are obtained through use of reduced Verma modules and Weyl group symmetry. Expansions of these are given which determine the particular representations present and results such as dimensions of superconformal multiplets. By restriction of variables various `blind' characters are also obtained. Limits, corresponding to reduction to particular subgroups, in the characters isolate contributions from particular subsets of multiplets and in many cases simplify the results considerably. As a special case, the index counting short and semi-short multiplets which do not form long multiplets found recently is shown to be related to particular cases of reduced characters. Partition functions of N=4 super Yang Mills are investigated. Through analysis of these, exact formulae are obtained for counting half and some quarter BPS operators in the free case. Similarly, partial results for the counting of semi-short operators are given. It is also shown in particular examples how certain short operators which one might combine to form long multiplets due to group theoretic considerations may be protected dynamically.

72 pages, uses harvmac

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• Counting BPS operators in N=4 SYM
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• The complete one-loop dilatation operator of planar real beta-deformed N=4 SYM theory
• Decoupling limits of N=4 super Yang-Mills on R x S^3
• Superspace conformal field theory
• Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index
• Permutation Centralizer Algebras and Multi-Matrix Invariants
• Superconformal partial waves in Grassmannian field theories
• Supergravitons from one loop perturbative N=4 SYM
• The Complete One-Loop Dilation Operator of N=2 SuperConformal QCD
• Notes on Super Killing Tensors
• 4D and 2D superconformal index with surface operator
• N=2 Moduli of AdS4 vacua: A fine-print study
• A note on N=8 counterterms
• Precision Spectroscopy and Higher Spin symmetry in the ABJM model
• BPS operators in $\mathcal{N}=4$ $SO(N)$ super Yang-Mills theory: plethysms, dominoes and words
• Finite N Index and Angular Momentum Bound from Gravity
• Flavour singlets in gauge theory as Permutations
• Asymptotic counting of BPS operators in superconformal field theories
• Bootstrapping mixed correlators in $\mathcal{N}=4$ Super Yang-Mills
• Two-Loop Spectroscopy of Short ABJM Operators
• Negative anomalous dimensions in N=4 SYM
• Refined Counting of Necklaces in One-loop $\mathcal{N}=4$ SYM
• One-Loop Free Energy of Tensionless Type IIB String in AdS${}_5\times$S${}^5$
• Group-Theoretical Classification of BPS and Possibly Protected States in D=4 Conformal Supersymmetry
• Complexity for superconformal primaries from BCH techniques
• Non-perturbative aspects of gauge and string theories and their holographic relations
• $\mathcal{N}=4$ SYM, (super)-polynomial rings and emergent quantum mechanical symmetries
• Explicit Character Formulae for Positive Energy UIRs of D=4 Conformal Supersymmetry
• Some aspects of conformal $\mathcal{N}=4$ SYM four point function
• Exploring Free Matrix CFT Holographies at One-Loop
• A hitchhiker's guide to quantum field theoretic aspects of $\mathcal{N}=4$ SYM theory and its deformations