Hints of Integrability Beyond the Planar Limit: Nontrivial Backgrounds
arXiv:0911.0967 · doi:10.1007/JHEP01(2010)014
Abstract
The problem of computing the anomalous dimensions of a class of (nearly) half-BPS operators with a large R-charge is reduced to the problem of diagonalizing a Cuntz oscillator chain. Due to the large dimension of the operators we consider, non-planar corrections must be summed to correctly construct the Cuntz oscillator dynamics. These non-planar corrections do not represent quantum corrections in the dual gravitational theory, but rather, they account for the backreaction from the heavy operator whose dimension we study. Non-planar corrections accounting for quantum corrections seem to spoil integrability, in general. It is interesting to ask if non-planar corrections that account for the backreaction also spoil integrability. We find a limit in which our Cuntz chain continues to admit extra conserved charges suggesting that integrability might survive.
25+1 pages; references added; v3: minor changes, references added
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- Quarter BPS classified by Brauer algebra
- LLM Magnons
- Exciting LLM Geometries
- Shaping up BPS States with Matrix Model Saddle Points
- Splitting of Folded Strings in AdS_4*CP^3