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

TL;DR

This paper explores the connection between large spin string states in AdS/CFT and Landau-Lifshitz equations, showing a universal effective description of string energies and SYM anomalous dimensions in certain sectors.

Contribution

It generalizes previous work to include SU(3) and SL(2) sectors, establishing a leading-order equivalence between string sigma models and SYM dilatation operators via Landau-Lifshitz equations.

Findings

String sigma model equations reduce to matrix Landau-Lifshitz equations at large spins.

SYMs one-loop dilatation operator matches the Landau-Lifshitz description.

Universal leading order correspondence between string energies and SYM anomalous dimensions.

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.