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

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.

LaTeX, 50 pages, 1 figure. v2: References added, minor corrections. 54 pages. v3: Few changes. One paragraph added at the end of section 3. 55 pages

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• Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations
• Two-loop commuting charges and the string/gauge duality
• Bethe ansatz and fluctuations in SU(3) Yang-Mills operators
• The Circular, Elliptic Three Spin String from the SU(3) Spin Chain
• Pulsating strings in warped AdS_6 x S^4 geometry

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