BMN Gauge Theory as a Quantum Mechanical System

Details BMN Gauge Theory as a Quantum Mechanical System BMN Gauge Theory as a Quantum Mechanical System

2002-12-20

arxiv.org/abs/hep-th/0212269v3

Phys.Lett.B558:229-237,2003

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, v2: minor changes, v3: typo corrected, to appear in Phys. Lett. B

Scientific paper

10.1016/S0370-2693(03)00269-7

We rigorously derive an effective quantum mechanical Hamiltonian from N=4 gauge theory in the BMN limit. Its eigenvalues yield the exact one-loop anomalous dimensions of scalar two-impurity BMN operators for all genera. It is demonstrated that this reformulation vastly simplifies computations. E.g. the known anomalous dimension formula for genus one is reproduced through a one-line calculation. We also efficiently evaluate the genus two correction, finding a non-vanishing result. We comment on multi-trace two-impurity operators and we conjecture that our quantum-mechanical reformulation could be extended to higher quantum loops and more impurities.

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