Giant graviton oscillators
Copyright policy )Giant graviton oscillators
We study the action of the dilatation operator on restricted Schur polynomials labeled by Young diagrams with p long columns or p long rows. A new version of Schur-Weyl duality provides a powerful approach to the computation and manipulation of the symmetric group operators appearing in the restricted Schur polynomials. Using this new technology, we are able to evaluate the action of the one loop dilatation operator. The result has a direct and natural connection to the Gauss Law constraint for branes with a compact world volume. We find considerable evidence that the dilatation operator reduces to a decoupled set of harmonic oscillators. This strongly suggests that integrability in N=4 super Yang-Mills theory is not just a feature of the planar limit, but extends to other large N but non-planar limits.
72 pages
- Stellenbosch University South Africa
- National Institute for Theoretical Physics South Africa
- University of the Witwatersrand South Africa
High Energy Physics - Theory, gauge-gravity correspondence, integrable field theories, Symmetric groups, \(1/N\) expansion, FOS: Physical sciences, Groups and algebras in quantum theory and relations with integrable systems, Representations of finite symmetric groups, Quantum field theory on curved space or space-time backgrounds, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Yang-Mills and other gauge theories in quantum field theory, Perturbative methods of renormalization applied to problems in quantum field theory, Finite-dimensional groups and algebras motivated by physics and their representations, AdS-CFT correspondence, High Energy Physics - Theory (hep-th), Gravitational interaction in quantum theory
High Energy Physics - Theory, gauge-gravity correspondence, integrable field theories, Symmetric groups, \(1/N\) expansion, FOS: Physical sciences, Groups and algebras in quantum theory and relations with integrable systems, Representations of finite symmetric groups, Quantum field theory on curved space or space-time backgrounds, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Yang-Mills and other gauge theories in quantum field theory, Perturbative methods of renormalization applied to problems in quantum field theory, Finite-dimensional groups and algebras motivated by physics and their representations, AdS-CFT correspondence, High Energy Physics - Theory (hep-th), Gravitational interaction in quantum theory
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