Abstract
I present a summary of hep-th/0404215, which suggested a novel way of organizing the dilatation operator D of planar \( \mathcal{N}\) = 4 SYM in the SU(2) sector. Instead of the usual perturbative expansion in powers of λ, we split D into parts D(n) according to the number n of independent pairwise interactions between spins at different sites. The BMN limit fixes D(1) completely, and it has regular expansions at both small and large values of λ. Anomalous dimensions of “long” operators in the two-scalar sector then generically scale as √λ at large λ, i.e. in the same way as energies of semiclassical states in the dual AdS5 ×S5 string theory.
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References
A. V. Ryzhov and A. A. Tseytlin, “Towards the exact dilatation operator of N=4 super Yang-Mills theory,” hep-th/0404215.
M. Kruczenski, “Spin chains and string theory,” hep-th/0311203.
M. Kruczenski, A. V. Ryzhov and A. A. Tseytlin, “Large spin limit of AdS5 × S5 string theory and low energy expansion of ferromagnetic spin chains,” hep-th/0403120.
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Ryzhov, A.V. (2005). Towards the Exact Dilatation Operator of \( \mathcal{N}\) = 4 Super Yang-Mills Theory. In: Baulieu, L., de Boer, J., Pioline, B., Rabinovici, E. (eds) String Theory: From Gauge Interactions to Cosmology. NATO Science Series II: Mathematics, Physics and Chemistry, vol 208. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3733-3_26
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DOI: https://doi.org/10.1007/1-4020-3733-3_26
Publisher Name: Springer, Dordrecht
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