Lattice super-Yang-Mills: A virial approach to operator dimensions

Curtis G. Callan, Jonathan Heckman, Tristan McLoughlin, Ian Swanson

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


The task of calculating operator dimensions in the planar limit of N = 4 super-Yang-Mills theory can be vastly simplified by mapping the dilatation generator to the Hamiltonian of an integrable spin chain. The Bethe ansatz has been used in this context to compute the spectra of spin chains associated with various sectors of the theory which are known to decouple in the planar (large- Nc) limit. These techniques are powerful at leading order in perturbation theory but become increasingly complicated beyond one loop in the 't Hooft parameter λ = gYM2 Nc, where spin chains typically acquire long-range (non-nearest-neighbor) interactions. In certain sectors of the theory, moreover, higher-loop Bethe ansätze do not even exist. We develop a virial expansion of the spin chain Hamiltonian as an alternative to the Bethe ansatz methodology, a method which simplifies the computation of dimensions of multi-impurity operators at higher loops in λ. We use these methods to extract previously reported numerical gauge theory predictions near the BMN limit for comparison with corresponding results on the string theory side of the AdS/CFT correspondence. For completeness, we compare our virial results with predictions that can be derived from current Bethe ansatz technology.

Original languageEnglish (US)
Pages (from-to)180-206
Number of pages27
JournalNuclear Physics B
Issue number1-2
StatePublished - Nov 22 2004

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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