Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations

TL;DR

The paper investigates the AdS/CFT correspondence in the large-spin limit, focusing on the SU(3) and SL(2) sectors of AdS5×S5 string states and their dual N=4 SYM operators. By reformulating the string action in a large-spin regime and employing spin-chain coherent states, the authors derive matrix Landau-Lifshitz-type actions for both the string and gauge theory sides, and show a universal leading-order equivalence of string energies and SYM anomalous dimensions, including matching integrable structures. The work extends previous SU(2) results to more general sectors, clarifying when a semi-classical sigma-model description is valid and highlighting the role of vacuum choice in non-holomorphic SO(6) sectors. These results strengthen the link between semiclassical string dynamics and one-loop gauge-theory integrable spin chains, with implications for understanding interpolating functions and pulsating/string regimes.

Abstract

We consider AdS_5 x S^5 string states with several large angular momenta along AdS_5 and S^5 directions which are dual to single-trace Super-Yang-Mills (SYM) operators built out of chiral combinations of scalars and covariant derivatives. In particular, we focus on the SU(3) sector (with three spins in S^5) and the SL(2) sector (with one spin in AdS_5 and one in S^5), generalizing recent work hep-th/0311203 and hep-th/0403120 on the SU(2) sector with two spins in S^5. We show that, in the large spin limit and at the leading order in the effective coupling expansion, the string sigma model equations of motion reduce to matrix Landau-Lifshitz equations. We then demonstrate that the coherent-state expectation value of the one-loop SYM dilatation operator restricted to the corresponding sector of single trace operators is also effectively described by the same equations. This implies a universal leading order equivalence between string energies and SYM anomalous dimensions, as well as a matching of integrable structures. We also discuss the more general 5-spin sector and comment on SO(6) states dual to non-chiral scalar operators.