Quantizing three-spin string solution in AdS_5 x S^5

TL;DR

This paper studies a classical string solution in AdS_5 x S^5, explores its stability and energy expansion, and tests a conjecture that classical energy formulas can predict anomalous dimensions in dual SYM theory.

Contribution

It introduces a specific non-supersymmetric string solution and analyzes its energy and stability, proposing a link to gauge theory anomalous dimensions and testing quantum corrections.

Findings

The classical energy admits an expansion in the effective coupling g_eff.

The solution is stable for J' > 3/2 J.

Quantum corrections are found to be subleading at large J'.

Abstract

As was recently found in hep-th/0304255, there exists a simple non-supersymmetric classical solution describing a closed string rotating in S^5 and located at the center of AdS_5. It is parametrized by the angular momentum J of the center of mass and two equal SO(6) angular momenta J' in the two other orthogonal rotation planes. The dual N=4 SYM operators should be scalar operators in SU(4) representations [0,J-J',2J'] or [J'-J,0,J'+J]. This solution is stable if J' > 3/2 J and for large J + 2 J' its classical energy admits an expansion in positive powers of g_eff = \lambda/(J + 2 J')^2: E= J + 2 J' + g_eff J' + ... . This suggests a possibility of a direct comparison with perturbative SYM results for the corresponding anomalous dimensions in the sector with g_eff << 1, by analogy with the BMN case. We conjecture that all quantum sigma model string corrections are then subleading at large J', so that the classical formula for the energy is effectively exact to all orders in \lambda. It could then be interpolated to weak coupling, representing a prediction for the anomalous dimensions on the SYM side. We test this conjecture by computing the 1-loop superstring sigma model correction to the classical energy.