BPS Operators in N=4 SYM: Calogero Models and 2D Fermions

Abstract

A connection between the gauge fixed dynamics of protected operators in superconformal Yang-Mills theory in four dimensions and Calogero systems is established. This connection generalizes the free Fermion description of the chiral primary operators of the gauge theory formed out of a single complex scalar to more general operators. In particular, a detailed analysis of protected operators charged under an su(1|1)contained in psu(2,2|4) is carried out and a class of operators is identified, whose dynamics is described by the rational super-Calogero model. These results are generalized to arbitrary BPS operators charged under an su(2|3) of the superconformal algebra. Analysis of the non-local symmetries of the super-Calogero model is also carried out, and it is shown that symmetry for a large class of protected operators is a contraction of the corresponding Yangian algebra to a loop algebra.

29 pages, 3 figures

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Cited by in corpus (13)

• Physics and Mathematics of Calogero particles
• Diagonal multi-matrix correlators and BPS operators in N=4 SYM
• Calogero models and nonlocal conformal transformations
• Yangians, S-matrices and AdS/CFT
• Free particles from Brauer algebras in complex matrix models
• Quantum SU(2$|$1) supersymmetric Calogero-Moser spinning systems
• Solitons and giants in matrix models
• Jain States in a Matrix Theory of the Quantum Hall Effect
• Review of AdS/CFT Integrability, Chapter VI.2: Yangian Algebra
• Symmetry and Integrability of Non-Singlet Sectors in Matrix Quantum Mechanics
• Sutherland Models for Complex Reflection Groups
• Aspects of Integrability in N =4 SYM
• "Non-renormalization" without supersymmetry