TY - JOUR

T1 - Lattice super-Yang-Mills

T2 - A virial approach to operator dimensions

AU - Callan, Curtis G.

AU - Heckman, Jonathan

AU - McLoughlin, Tristan

AU - Swanson, Ian

N1 - Funding Information:
This work was supported in part by US Department of Energy grants DE-FG02-91ER40671 (Princeton) and DE-FG03-92-ER40701 (Caltech).

PY - 2004/11/22

Y1 - 2004/11/22

N2 - 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.

AB - 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.

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U2 - 10.1016/j.nuclphysb.2004.09.010

DO - 10.1016/j.nuclphysb.2004.09.010

M3 - Article

AN - SCOPUS:7444269581

SN - 0550-3213

VL - 701

SP - 180

EP - 206

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 1-2

ER -