Spiky strings and single trace operators in 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.

23 pages, 5 figures. v2: References and comments added

References in corpus (10)

• Integrability in QCD and beyond
• Semiclassical relativistic strings in S^5 and long coherent operators in N=4 SYM theory
• Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations
• Classical/quantum integrability in non-compact sector of AdS/CFT
• SL(2) spin chain and spinning strings on AdS_5xS^5
• Spin chain sigma models with fermions
• Semiclassical Strings on AdS_5 x S^5/Z_M and Operators in Orbifold Field Theories
• Open Semiclassical Strings and Long Defect Operators in AdS/dCFT Correspondence
• Semiclassical strings in AdS_5 x S^5 and scalar operators in N=4 SYM theory
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