Semiclassical relativistic strings in S^5 and long coherent operators in N=4 SYM theory

TL;DR

This paper develops a sigma model approach to relate long, non-holomorphic operators in N=4 SYM theory to semiclassical string solutions in S^5, extending previous rigid string analyses to pulsating strings with explicit energy calculations.

Contribution

It introduces a systematic expansion of the string sigma model for pulsating strings in S^5 and maps these solutions to corresponding coherent operators in N=4 SYM theory.

Findings

Established a map between string profiles and SYM operators.

Derived explicit forms of dual operators for pulsating strings.

Simplified energy computations using action--angle variables.

Abstract

We consider the low energy effective action corresponding to the 1-loop, planar, dilatation operator in the scalar sector of N=4 SU(N) SYM theory. For a general class of non-holomorphic ``long'' operators, of bare dimension L>>1, it is a sigma model action with 8-dimensional target space and agrees with a limit of the phase-space string sigma model action describing generic fast-moving strings in the S^5 part of AdS_5 x S^5. The limit of the string action is taken in a way that allows for a systematic expansion to higher orders in the effective coupling $\lambda/L^2$. This extends previous work on rigid rotating strings in S^5 (dual to operators in the SU(3) sector of the dilatation operator) to the case when string oscillations or pulsations in S^5 are allowed. We establish a map between the profile of the leading order string solution and the structure of the corresponding coherent, ``locally BPS'', SYM scalar operator. As an application, we explicitly determine the form of the non-holomorphic operators dual to the pulsating strings. Using action--angle variables, we also directly compute the energy of pulsating solutions, simplifying previous treatments.