Algebraic Curve for the SO(6) Sector of AdS/CFT

Abstract

We construct the general algebraic curve of degree four solving the classical sigma model on R × S 5 . Up to two loops it coincides with the algebraic curve for the dual sector of scalar operators in N = 4 SYM, also constructed here. We explicitly reproduce some particular solutions.

A large spin limit of strings on in a non-compact sector

“…Here, we would like to emphasize that our point is to show a sector-wise correspondence to the gauge theory for large S, as in the Frolov-Tseytlin limit [7,8,[12][13][14][15][16]: The log S scaling holds not only for multi-soliton solutions, whose variation from the ground state is relatively small, but also for general quasi-periodic solutions, which could be far apart from the ground state. Such a sector-wise correspondence would also be useful to study the correspondence of the operators/solutions between the gauge/string sides, which is generally quite non-trivial (e.g., [38]).…”

“…This suggests another interesting window to explore the AdS/CFT correspondence. Our analysis may be extended to other non-compact sectors along the line of [13][14][15][16][17].…”

Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings

“…The finite size Bethe ansatz equations that we have obtained, including the 1/L correction, may allow for a comparison with the string dynamics along the lines of [26,27,28].…”

Double scaling and finite size corrections in spin chain

“…The appropriate thermodynamical limit in terms of non-hyperelliptic curve, corresponding to very long operators in SYM was constructed in particular sectors in [4,7,20,37] and for the full psu(2, 2|4) SYM chain in [11]. Finding the finite size corrections to these solutions might be extremely useful for getting some clues for the quantization of the string sigma model on the other side of AdS/CFT correspondence.…”