Spiky strings and single trace operators in gauge theories

TL;DR

This work proposes a dual description for large-N single-trace gauge-theory operators, mapping them to rotating strings with spikes in AdS_5. By constructing explicit spike solutions in both flat space and AdS, deriving their exact and asymptotic properties, and formulating an effective classical mechanics for spike motion, the authors connect bulk spike dynamics to a boundary coherent-state spin-chain description. They show that, at 1-loop, the field theory results match the functional form of the bulk predictions up to coupling constants, highlighting a robust boundary–bulk dictionary. The study also outlines a tentative interpretation of the radial AdS coordinate in field theory terms and suggests that moving spikes in other directions could describe operators with different derivatives, indicating a broad and generic avenue for understanding the string description of large-N gauge theories.

Abstract

We consider single trace operators of the form O_{m_1 ... m_n} = tr D_+^{m_1} F ... D_+^{m_n} F which are common to all gauge theories. We argue that, when all m_i are equal and large, they have a dual description as strings with cusps, or spikes, one for each field F. In the case of N=4 SYM, we compute the energy as a function of angular momentum by finding the corresponding solutions in AdS_5 and compare with a 1-loop calculation of the anomalous dimension. As in the case of two spikes (twist two operators), there is agreement in the functional form but not in the coupling constant dependence. After that, we analyze the system in more detail and find an effective classical mechanics describing the motion of the spikes. In the appropriate limit, it is the same (up to the coupling constant dependence) as the coherent state description of linear combinations of the operators O_{m_1 ... m_n} such that all m_i are equal on average. This agreement provides a map between the operators in the boundary and the position of the spikes in the bulk. We further suggest that moving the spikes in other directions should describe operators with derivatives other than D_+ indicating that these ideas are quite generic and should help in unraveling the string description of the large-N limit of gauge theories.